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The document discusses constructing a quadrilateral with the maximum area given the lengths of its four sides. It presents the objective of studying how to arrange the sides and adjust the angles. The method described is to construct the quadrilateral within a circle since the area is maximized when the opposite angles sum to 180 degrees. Formulas are derived relating the radius, angles at the center and between radii, and side lengths of the inscribed quadrilateral with maximum area.
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Present(Eng)
The document discusses constructing a quadrilateral with the maximum area given the lengths of its four sides. It presents the following key points:
1) The maximum area quadrilateral can be constructed by arranging the sides in a circle, with the opposite angles summing to 180 degrees.
2) The relationships between the radius of the circle, the angles between sides, and the side lengths are described by formulas using trigonometry.
3) Given the four side lengths, the maximum area quadrilateral can be constructed in a circle by first calculating the radius, then drawing the sides based on the radius and angle formulas.
Present(Pbwik)I
The document discusses constructing the quadrilateral with the maximum area given the lengths of its four sides. It presents five key results:
1) The relationship between angles and sides of the quadrilateral when constructed in a circle with the angle between two adjacent sides.
2) The relationship among the radius of the circle, the angle, and the lengths of sides close to the angle.
3) The relationship between the angle at the center of the circle and the length of sides and radius.
4) How to construct the maximum area quadrilateral by drawing the sides in a circle based on calculated radii and angles.
5) The relationship between the angle at the center of the circle and the angles in the quadrilateral.
Present(Pbwik)I
1) The document discusses constructing the quadrilateral with the maximum area given the lengths of its four sides.
2) It presents methods for determining the radius of the enclosing circle, the angles between sides, and the relationship between these angles and the side lengths.
3) The key results are relationships that allow constructing the maximum-area quadrilateral in a circle by drawing radii and the angles between them based on the given side lengths.
C2.0 Triangles
Triangles
Introduction
Sum of the angles of a triangle
Types of triangles
Altitude, Median and Angle Bisector
Congruence of triangles
Sides opposite congruent angles
C4: perimeter and area
Chapter 4 Perimeter And Area
4.1 Perimeter
4.2 Square
4.3 Rectangle
4.4 Parallelogram
4.5 Triangle
4.6 Trapezoids
4.7 Circles
Area & volume
This document presents information about various geometric shapes and formulas for calculating dimensions such as perimeter, area, surface area, and volume. It defines length, width, and height. Formulas are provided for calculating the perimeter and area of rectangles, squares, triangles, parallelograms, trapezoids, and circles. Surface area and volume formulas are given for cubes, cuboids, cylinders, cones, spheres, and other three-dimensional shapes.
Perimeter
This document discusses how to calculate the perimeter of rectangles and squares. It provides examples of calculating perimeters given the length and width of rectangles, or given the side length of squares. Formulas are provided: For rectangles, the perimeter is 2 * length + 2 * width. For squares, the perimeter is 4 * the side length. An example word problem is also worked out calculating the perimeter of a rectangular plot of land and the cost of fencing wire around it.
Perimeter
The document defines perimeter and provides formulas for calculating the perimeter of rectangles, squares, and triangles. It explains that perimeter is the distance around a two-dimensional shape. For rectangles, the perimeter formula is P=2(length+breadth). For squares, the formula is P=4xside. For triangles, the formula is P=a+b+c, where a, b, and c are the lengths of the three sides. An example problem calculates the perimeter of a triangular plot of land that is to be fenced with four rounds of wire.
Recommended
Present(Eng)
The document discusses constructing a quadrilateral with the maximum area given the lengths of its four sides. It presents the following key points:
1) The maximum area quadrilateral can be constructed by arranging the sides in a circle, with the opposite angles summing to 180 degrees.
2) The relationships between the radius of the circle, the angles between sides, and the side lengths are described by formulas using trigonometry.
3) Given the four side lengths, the maximum area quadrilateral can be constructed in a circle by first calculating the radius, then drawing the sides based on the radius and angle formulas.
Present(Pbwik)I
The document discusses constructing the quadrilateral with the maximum area given the lengths of its four sides. It presents five key results:
1) The relationship between angles and sides of the quadrilateral when constructed in a circle with the angle between two adjacent sides.
2) The relationship among the radius of the circle, the angle, and the lengths of sides close to the angle.
3) The relationship between the angle at the center of the circle and the length of sides and radius.
4) How to construct the maximum area quadrilateral by drawing the sides in a circle based on calculated radii and angles.
5) The relationship between the angle at the center of the circle and the angles in the quadrilateral.
Present(Pbwik)I
1) The document discusses constructing the quadrilateral with the maximum area given the lengths of its four sides.
2) It presents methods for determining the radius of the enclosing circle, the angles between sides, and the relationship between these angles and the side lengths.
3) The key results are relationships that allow constructing the maximum-area quadrilateral in a circle by drawing radii and the angles between them based on the given side lengths.
C2.0 Triangles
Triangles
Introduction
Sum of the angles of a triangle
Types of triangles
Altitude, Median and Angle Bisector
Congruence of triangles
Sides opposite congruent angles
C4: perimeter and area
Chapter 4 Perimeter And Area
4.1 Perimeter
4.2 Square
4.3 Rectangle
4.4 Parallelogram
4.5 Triangle
4.6 Trapezoids
4.7 Circles
Area & volume
This document presents information about various geometric shapes and formulas for calculating dimensions such as perimeter, area, surface area, and volume. It defines length, width, and height. Formulas are provided for calculating the perimeter and area of rectangles, squares, triangles, parallelograms, trapezoids, and circles. Surface area and volume formulas are given for cubes, cuboids, cylinders, cones, spheres, and other three-dimensional shapes.
Perimeter
This document discusses how to calculate the perimeter of rectangles and squares. It provides examples of calculating perimeters given the length and width of rectangles, or given the side length of squares. Formulas are provided: For rectangles, the perimeter is 2 * length + 2 * width. For squares, the perimeter is 4 * the side length. An example word problem is also worked out calculating the perimeter of a rectangular plot of land and the cost of fencing wire around it.
Perimeter
The document defines perimeter and provides formulas for calculating the perimeter of rectangles, squares, and triangles. It explains that perimeter is the distance around a two-dimensional shape. For rectangles, the perimeter formula is P=2(length+breadth). For squares, the formula is P=4xside. For triangles, the formula is P=a+b+c, where a, b, and c are the lengths of the three sides. An example problem calculates the perimeter of a triangular plot of land that is to be fenced with four rounds of wire.
Perimeter
The document defines perimeter as the distance around a polygon and explains that to find the perimeter of a polygon you add up the lengths of all the sides. It provides examples of calculating the perimeter of various shapes including triangles, squares, rectangles, pentagons, and hexagons. Formulas and step-by-step workings are shown for finding the perimeter when given the measurements of the sides.
Perimeter
The document defines perimeter as the total length of the sides surrounding a shape. It provides the formulas to calculate the perimeter of common shapes like triangles, squares, rectangles, pentagons, and circles. For each shape, it gives an example with measurements and calculates the perimeter. The perimeter of a triangle is the sum of the lengths of its three sides. The perimeter of a square is the sum of the lengths of its four equal sides. The perimeter of a rectangle is calculated by adding the lengths of all four of its sides.
11.6 area of reg polygons
The document discusses the formulas and methods for calculating the area of regular polygons. It defines key terms like the center, radius, apothem, and central angle. It presents the theorem that the area of a regular polygon is equal to half the product of the apothem and perimeter. Examples are given of calculating areas of regular polygons by using the apothem, perimeter, and this area formula. Methods are described for finding the apothem or side length when they are not given.
11.3 perimeters and areas of similar figures
This document discusses perimeters and areas of similar polygons. It states that the ratio of perimeters of similar polygons is equal to the ratio of corresponding side lengths, while the ratio of their areas is equal to the ratio of the squares of corresponding side lengths. It provides examples calculating perimeter and area ratios of similar shapes and using them to solve real-world problems.
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- Formulas for calculating perimeter and area of common shapes like triangles, rectangles, parallelograms, trapezoids, circles, and composite figures
- Examples of using definitions and formulas to solve perimeter and area problems for single and composite geometric shapes.
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The document discusses perimeter and provides examples of calculating perimeter for different shapes like triangles, rectangles, squares, polygons, and irregular figures. It defines perimeter as the distance around a two-dimensional shape or the boundary of a plane figure. Several word problems are included that require calculating perimeter based on given lengths or finding unknown lengths based on the total perimeter.
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The document discusses teaching concepts related to shape and space for Year 4, including:
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The document discusses perimeter and how to calculate it for different shapes. It defines perimeter as the distance around a shape and provides formulas to calculate perimeter for rectangles and polygons. For rectangles, the perimeter formula is P=2l+2w, where l is the length and w is the width. For polygons, you add up the lengths of all the sides. The document also shows how to use algebra to solve for missing side lengths when given the perimeter.
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This document discusses the Pythagorean theorem. It begins with an introduction of the theorem, followed by examples of using it to solve for the length of a triangle's hypotenuse given the lengths of the other two sides. The document then provides task cards with real world problems for students to solve using the Pythagorean theorem. It concludes with a post-test asking students to use the theorem to find hypotenuse lengths.
Examples Of Perimeter
The document provides 3 examples of perimeter calculations: 1) Finding the perimeter of a triangle with sides of 5, 9, and 11 cm, which equals 25 cm. 2) Calculating the perimeter of a rectangle and two similar squares shown in a diagram, which equals 34 cm. 3) Determining the cost of barbed wire to fence a 120m x 120m square garden, which is RM5280 using 480m of fencing at RM11 per meter.
Mensuration
It will surely help you in completing your projects, holiday homeworks and activities. It includes a lot of things- acknowledgements, quote-unquote as well as introduction. Hope it helps you
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This document discusses how to find the area and perimeter of squares, rectangles, and triangles. It provides the formulas for calculating the area of a rectangle as length x width, the area of a square as the length of a side squared, and the area of a triangle as half the base x height. It also gives the formulas for finding the perimeter of a rectangle and square. Several examples are worked through applying these formulas to find missing dimensions.
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This document discusses geometry concepts related to two-dimensional shapes including perimeter and area. It defines perimeter as the distance around the edge of a shape and area as the space inside a shape. For squares, the perimeter is calculated as 4 times the side length and the area as side length squared. For rectangles, the perimeter is the sum of all sides and the area is width multiplied by height. Examples are provided for calculating perimeters and areas of squares and rectangles.
Pythagorean theorem powerpoint
1) The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It can be used to find the length of any side of a right triangle if the other two sides are known.
2) The distance formula calculates the distance between two points in a plane by using the differences between their x- and y-coordinates, based on the Pythagorean theorem. You find the distance by taking the square root of the sum of the squared differences of the x- and y-coordinates.
3) The example calculates the distance between points (4, -3) and (7, 2) using the distance formula
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The document discusses the formulas for calculating the areas of various shapes. The formulas are:
Area of a rectangle = length x width
Area of a square = side x side
Area of a triangle = (base x height)/2
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A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object
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The document defines perimeter as the distance around a polygon and explains that to find the perimeter of a polygon you add up the lengths of all the sides. It provides examples of calculating the perimeter of various shapes including triangles, squares, rectangles, pentagons, and hexagons. Formulas and step-by-step workings are shown for finding the perimeter when given the measurements of the sides.
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The document defines perimeter as the total length of the sides surrounding a shape. It provides the formulas to calculate the perimeter of common shapes like triangles, squares, rectangles, pentagons, and circles. For each shape, it gives an example with measurements and calculates the perimeter. The perimeter of a triangle is the sum of the lengths of its three sides. The perimeter of a square is the sum of the lengths of its four equal sides. The perimeter of a rectangle is calculated by adding the lengths of all four of its sides.
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The document discusses the formulas and methods for calculating the area of regular polygons. It defines key terms like the center, radius, apothem, and central angle. It presents the theorem that the area of a regular polygon is equal to half the product of the apothem and perimeter. Examples are given of calculating areas of regular polygons by using the apothem, perimeter, and this area formula. Methods are described for finding the apothem or side length when they are not given.
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This document discusses perimeters and areas of similar polygons. It states that the ratio of perimeters of similar polygons is equal to the ratio of corresponding side lengths, while the ratio of their areas is equal to the ratio of the squares of corresponding side lengths. It provides examples calculating perimeter and area ratios of similar shapes and using them to solve real-world problems.
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This document provides an introduction to basic geometry concepts including:
- Euclid's undefined terms of point, line, and plane
- Definitions of basic shapes such as rays, line segments, angles, and polygons
- Classifications of quadrilaterals and regular polygons
- Formulas for calculating perimeter and area of common shapes like triangles, rectangles, parallelograms, trapezoids, circles, and composite figures
- Examples of using definitions and formulas to solve perimeter and area problems for single and composite geometric shapes.
Perimeter
The document discusses perimeter and provides examples of calculating perimeter for different shapes like triangles, rectangles, squares, polygons, and irregular figures. It defines perimeter as the distance around a two-dimensional shape or the boundary of a plane figure. Several word problems are included that require calculating perimeter based on given lengths or finding unknown lengths based on the total perimeter.
Shape & Space
The document discusses teaching concepts related to shape and space for Year 4, including:
1. Two-dimensional shapes and calculating their perimeter and area, such as squares, rectangles, and triangles.
2. Three-dimensional shapes like cubes and cuboids, and calculating their volume.
3. Key formulas for calculating perimeter, area, and volume of different shapes. Examples of problems are provided to help teach these concepts.
Perimeter
The document discusses perimeter and how to calculate it for different shapes. It defines perimeter as the distance around a shape and provides formulas to calculate perimeter for rectangles and polygons. For rectangles, the perimeter formula is P=2l+2w, where l is the length and w is the width. For polygons, you add up the lengths of all the sides. The document also shows how to use algebra to solve for missing side lengths when given the perimeter.
Pythagorean theorem
This document discusses the Pythagorean theorem. It begins with an introduction of the theorem, followed by examples of using it to solve for the length of a triangle's hypotenuse given the lengths of the other two sides. The document then provides task cards with real world problems for students to solve using the Pythagorean theorem. It concludes with a post-test asking students to use the theorem to find hypotenuse lengths.
Examples Of Perimeter
The document provides 3 examples of perimeter calculations: 1) Finding the perimeter of a triangle with sides of 5, 9, and 11 cm, which equals 25 cm. 2) Calculating the perimeter of a rectangle and two similar squares shown in a diagram, which equals 34 cm. 3) Determining the cost of barbed wire to fence a 120m x 120m square garden, which is RM5280 using 480m of fencing at RM11 per meter.
Mensuration
It will surely help you in completing your projects, holiday homeworks and activities. It includes a lot of things- acknowledgements, quote-unquote as well as introduction. Hope it helps you
1.4 Area and Perimeter
This document discusses how to find the area and perimeter of squares, rectangles, and triangles. It provides the formulas for calculating the area of a rectangle as length x width, the area of a square as the length of a side squared, and the area of a triangle as half the base x height. It also gives the formulas for finding the perimeter of a rectangle and square. Several examples are worked through applying these formulas to find missing dimensions.
CLASS IX MATHS PPT
The document discusses different types of 2D and 3D shapes. It defines rectangles, squares, triangles, and hexagons as plane or 2D figures. Cuboids, cubes, and cylinders are defined as solid or 3D figures. Solid figures are made up of plane surfaces or figures. The surface area of solids is calculated by finding the total area of these plane figures. Formulas are provided to calculate the surface area of cuboids and cubes. Practice questions are included for students to calculate surface areas of shapes based on given measurements.
1.5 Area and Circumference
This document discusses formulas for finding the area and circumference of circles. It defines pi (π) as the ratio of a circle's circumference to its diameter. The circumference can be found using the diameter or radius using the formulas C=πd or C=2πr. The area of a circle can be found using the formula A=πr^2. Examples are provided for finding the diameter, radius, or area given values for one of the other properties. Approximations of π may be used for practical purposes, but exact values should leave π as the symbol.
Pythagoras theorem
Pythagoras was an ancient Greek philosopher and mathematician born on the island of Samos in around 570 BC. He is best known for the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. While Pythagoras likely did not discover this theorem himself, he is credited as being the first to prove why it is true. The Pythagorean theorem is one of the earliest and most important theorems in mathematics.
Geometry: Perimeter and Area
This document discusses geometry concepts related to two-dimensional shapes including perimeter and area. It defines perimeter as the distance around the edge of a shape and area as the space inside a shape. For squares, the perimeter is calculated as 4 times the side length and the area as side length squared. For rectangles, the perimeter is the sum of all sides and the area is width multiplied by height. Examples are provided for calculating perimeters and areas of squares and rectangles.
Pythagorean theorem powerpoint
1) The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It can be used to find the length of any side of a right triangle if the other two sides are known.
2) The distance formula calculates the distance between two points in a plane by using the differences between their x- and y-coordinates, based on the Pythagorean theorem. You find the distance by taking the square root of the sum of the squared differences of the x- and y-coordinates.
3) The example calculates the distance between points (4, -3) and (7, 2) using the distance formula
Finding Area
The document discusses the formulas for calculating the areas of various shapes. The formulas are:
Area of a rectangle = length x width
Area of a square = side x side
Area of a triangle = (base x height)/2
Perimeter and Area of Polygons
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object
Perimeter
This document provides a lesson on calculating the perimeters of polygons. It begins by defining a polygon and perimeter. Students are shown how to calculate the perimeter of a rectangle by adding the length and width measurements. The formula for a rectangle's perimeter, 2 x length + 2 x width, is introduced. Other shapes where not all side measurements are needed, like squares, are discussed. Finally, students are given a challenge to calculate the perimeter of a more complex shape and express it in words and letters.
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Module 5 geometry of shape and size
This module discusses geometry concepts related to shape and size, including perimeter and circumference formulas. It will cover calculating the perimeter of common polygons like triangles, quadrilaterals, and polygons with more than 4 sides. It will also cover circumference formulas for circles. Students will learn to define basic geometric terms, state relevant formulas, and apply these concepts to solve real-world problems involving perimeter and circumference. The module contains sample problems and multi-step word problems for students to practice these skills.
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This document provides an introduction to geometry. It begins by defining geometry as the study of shapes and notes it is one of the oldest branches of mathematics. It discusses how modern geometry began with the Greeks over 2000 years ago and how Euclid of Alexandria wrote "The Elements", systematically recording all known geometry. Basic geometric terms like points, lines, planes, angles, and polygons are defined. Different types of polygons and quadrilaterals are classified. Methods for finding the perimeter and area of basic shapes like triangles, rectangles, parallelograms, trapezoids, and circles are presented. Composite figures made of multiple shapes are introduced. Several examples of calculating perimeters and areas of various geometric figures are provided.
17 GEOMETRY.ppt
This document provides an introduction to geometry. It begins by defining geometry as the study of shapes and notes it is one of the oldest branches of mathematics. It discusses how modern geometry began with the Greeks over 2000 years ago and how Euclid of Alexandria wrote "The Elements", systematically recording all known geometry. Basic geometric terms like points, lines, planes, angles, and polygons are defined. Different types of polygons and quadrilaterals are classified. Methods for finding the perimeter and area of basic shapes like triangles, rectangles, parallelograms, trapezoids, and circles are presented. Composite figures made of multiple shapes are introduced. Several examples of calculating perimeters and areas are worked through.
Maths Presentation 4th Group.pjgcjn hunptx
This document discusses concepts of area, perimeter, and volume. It defines each concept and provides formulas to calculate these measurements for different shapes like rectangles, triangles, circles, cylinders, spheres and other irregular shapes. Area is the measure of surface enclosed by a shape. Perimeter is the distance around a shape. Volume measures space occupied by 3D shapes. Formulas to calculate these values are given for various regular shapes. The conclusion restates the importance of understanding these concepts for analyzing properties of shapes.
Surface Area_Volume of Solid Figures.ppt
The document provides information about calculating the surface area of cylinders and cones. It begins by defining a cylinder and its components. It then derives the formula for the surface area of a cylinder by imagining unrolling the cylinder surface. The formula is presented as SA=2πr(r+h). An example problem applying this formula is shown. Methods for finding the surface area of cones are also presented, with the formula given as the area of the base plus the lateral area. Several examples problems demonstrate applying the surface area formulas for cylinders and cones.
Cones
A cone is a 3D geometric shape that tapers from a flat circular base to a single point called the apex. The formulas for the volume and surface area of a cone involve the radius of the base and the height or slant height. Word problems apply these formulas to calculate missing values like height, volume, or surface area when other values like radius or volume are given.
Chord of a Circle Definition Formula Theorem & Examples.pdf
Finding the chord of a circle is one of the most important terms in math. Learn what the chord of the circle is and how to use the chord length formula with examples and theorems.
Power point presentation PIYUSH BHANDARI
3-D shapes have length, width, and height. A cube has 6 faces, 12 edges, and 8 vertices. The surface area of a cube can be found by calculating the area of each face, which is the length squared, and multiplying by 6 since there are 6 faces. The surface area of other 3-D shapes like cuboids and cylinders can be found by calculating the total area of all faces, such as using the formula for a cuboid of 2 times the length times width plus 2 times the height times width plus 2 times the length times height. The surface area of a cylinder is 2 times pi times the radius times the height plus 2 times pi times the radius squared.
Math Geometry
The document provides information on geometry topics including angles, distance, area, and volume. It defines key concepts such as perpendicular lines, parallel lines, interior and exterior angles, circumference, arc length, perimeter, area of triangles, circles, quadrilaterals, and strategies for finding areas of irregular shapes. Examples are provided to illustrate formulas and problem-solving approaches for finding distances, midpoints, areas, and perimeters in various geometric figures.
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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- 1. Krittika Poksawat N0.2 Class M.6/4 Tatcha Tratornpisuttikul N0.12 Class M.6/4 Worawoot Sumontra N0.23 Class M.6/4 Mahidol Wittayanusorn Constructing the quadrilateral with the maximum area when given the lengths
- 2. Adviser Miss Nongluk Arpasuth Mr. Sunya Phumkumarn Constructing the quadrilateral with the maximum area when given the lengths
- 3. Introduction Currently, to find the area of any geometric figure is usually from any ready made figure. In another way, if the sides of figure are given then many geometric figures can be made. Our group will study how to construct maximal area figures especially in quadrilateral. The study is to examine that how the given four sides can be arranged and how to adjust the angles to construct a maximal area quadrilateral. Constructing the quadrilateral with the maximum area when given the lengths
- 5. ระยะเวลาในการดำเนินงาน From July 2007 to December 2007 Constructing the quadrilateral with the maximum area when given the lengths
- 6. that cos ( A+B) equal to 0 . So that Consider , the area of the quadrilateral Area = When given The area will be the maximum when Constructing the quadrilateral with the maximum area when given the lengths Method is the smallest That is we must construct the quadrilateral in the circle.
- 7. So that, we can find the maximum area Area = When given Constructing the quadrilateral with the maximum area when given the lengths Method
- 8. Consider, the quadrilateral with the sum of the opposite angle equal to 180 Given the quadrilateral mnop with the sides, a,b,c,d . Constructing the quadrilateral with the maximum area when given the lengths Method
- 9. Figure 1 Figure 2 consider figure 1 change to figure 2 we can suppose that the sum of the opposite angle must equal to Constructing the quadrilateral with the maximum area when given the lengths Method
- 10. Constructing the quadrilateral with the maximum area when given the lengths Method 1.)Consider the order of four sides we can calculate that the most of figure can be 3!or 6. And we found the sum of length of three sides of quadrilateral must more than another one. Thus every quadrilaterals can construct 6 figures. 2.)consider the order of four sides, we found that the 6 figure must have the same maximum area .Consider from the formula of maximum area when
- 11. consider triangle ADC จาก law of cosine then consider triangle ABC from law of cosine then … ..1 … ..2 (1) = (2) when Step finding the relation Constructing the quadrilateral with the maximum area when given the lengths Method
- 12. consider triangle AEC from law of cosine then … .(3) thus From 1=3 Finding radius of circle Constructing the quadrilateral with the maximum area when given the lengths Method
- 13. finding , , and giving is the angle between radii of circle in triangle CED is the angle between radii of circle in triangle AED is the angle between radii of circle in triangle AEB is the angle between radii of circle in triangle BEC Consider triangle CED of law of cosine then thus In the same way Finding the angle at the center of circle Constructing the quadrilateral with the maximum area when given the lengths Method
- 14. consider then … .(1) (1)+(2) thus … .(2) Finding the relation of angles Constructing the quadrilateral with the maximum area when given the lengths Method
- 15. when ผลการศึกษาที่ 1 Constructing the quadrilateral with the maximum area when given the lengths Relation between angles and the sides of quadrilateral in the circle when the angle is between two sides that are adjacent sides