Geometry
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This document discusses perimeter and area of polygons. It defines perimeter as the sum of the lengths of all sides of a polygon. Area is defined as the number of square units within a shape. Specifically: 1) It provides formulas for finding the perimeter and area of squares and rectangles. The perimeter of a square is 4 times the length of one side, and the area is the square of the length of one side. The area of a rectangle is length times width. 2) Examples are given to demonstrate calculating perimeters and areas of various polygons, including finding a pattern between side length and perimeter/area of squares. 3) The key formulas and concepts taught are finding perimeter, area of squares and
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1) Given: Scale ratio = 1 cm = 1 m
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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.
Geometric_Shapes_AreaWeb.ppt
This document defines and provides examples of different geometric shapes and how to calculate their areas. It discusses circles, including calculating area using the radius. It also covers polygons like triangles, quadrilaterals, and regular polygons. Formulas are provided for calculating the areas of circles, triangles, parallelograms, trapezoids, and finding missing side lengths using the Pythagorean theorem. Examples of applying these formulas to solve for areas and side lengths are also included.
Interim 4th review
The document provides examples and explanations for calculating the areas and volumes of various shapes, such as triangles, trapezoids, rectangles, circles, cylinders, and prisms. It also discusses finding the surface areas of shapes like pyramids and cylinders. The examples show setting up formulas, substituting values, and performing calculations to find the requested measurements.
Perimeter & area presentation
This document provides instructions and formulas for calculating the perimeter and area of rectangles and squares. It includes the objectives of finding perimeter and area using formulas, provides the relevant formulas, and includes example perimeter and area word problems to solve. Key information covered includes the definitions of perimeter and area, the perimeter and area formulas for rectangles and squares, and example activities applying the formulas.
Symmetry and Surface Area.pptxpptxpptxpptx
Symmetry and surface area are two distinct geometric concepts, but they are often considered in various contexts, such as geometry, mathematics, and even physics or engineering. Let's explore each concept:
### Symmetry:
**Symmetry** refers to a balanced and proportionate arrangement of parts or elements on either side of a dividing line or plane. In geometry, there are several types of symmetry:
1. **Line Symmetry (Reflection Symmetry):** A shape has line symmetry if one half of it is the mirror image of the other half when divided along a line. Common examples include squares, circles, and many letters of the alphabet.
2. **Rotational Symmetry:** A shape has rotational symmetry if it can be rotated about a point so that it looks exactly the same in multiple positions. For example, a circle has infinite rotational symmetry.
3. **Point Symmetry:** A shape has point symmetry if it looks the same when rotated 180 degrees about a central point. Not all shapes have point symmetry.
Symmetry is a fundamental concept in geometry and has applications in various fields, including art, design, and science.
### Surface Area:
**Surface Area** is the measure of the total area that covers the surface of a three-dimensional object. The formulas for calculating the surface area of common geometric shapes include:
1. **Cuboid or Rectangular Prism:**
\[SA = 2lw + 2lh + 2wh\]
2. **Cylinder:**
\[SA = 2\pi r^2 + 2\pi rh\]
3. **Sphere:**
\[SA = 4\pi r^2\]
4. **Cone:**
\[SA = \pi r^2 + \pi r \sqrt{r^2 + h^2}\]
5. **Pyramid:**
\[SA = \frac{1}{2}Pl + B\]
where \(P\) is the perimeter of the base, \(l\) is the slant height, and \(B\) is the base area.
Understanding surface area is crucial in various fields, especially in engineering, architecture, and physics, where it is essential for calculating materials needed for construction, heat transfer, and other physical properties.
In some cases, symmetry can simplify the calculation of surface area. For instance, symmetrical objects may have repeated patterns that can be leveraged to simplify the surface area calculation.
Both symmetry and surface area play important roles in geometry and have practical applications in real-world problem-solving.
AREA AND PERIMETER
This document defines and provides formulas for calculating the area and perimeter of basic shapes like triangles, squares, rectangles, and parallelograms. It also includes examples of using the formulas to find the area and perimeter of these shapes given specific dimensions. Key formulas included are that the perimeter of a triangle is the sum of its three sides, the area is 1/2 base x height, the perimeter of a square is 4 times the length of a side, and its area is the square of the side length. Formulas for rectangles and parallelograms relate the perimeter to sums of adjacent sides and the area to the product of base and height.
Obj. 49 Solid Geometry
Classify three-dimensional figures according to their properties.
Use nets and cross sections to analyze three-dimensional figures.
Extend midpoint and distance formulas to three dimensions
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.
p5-digitalfinalll-1.pptx areas..........
This document discusses the areas of different plane figures including squares, rectangles, triangles, parallelograms, trapezoids, and circles. It provides the formulas to calculate the area of each shape and works through examples of finding the area of a circular table and the floor area of a square room. The key formulas are: the area of a square is s^2, the area of a rectangle is length x width, the area of a triangle is 1/2 x base x height, the area of a parallelogram is base x height, the area of a trapezoid is 1/2 x (b1 + b2) x height, and the area of a circle is πr^
Ploygon (27 July).pdf
This document provides a lesson on polygons and calculating perimeter of squares. It begins with an introduction to polygons, defining them as closed, flat shapes made of straight lines with three or more sides. It then focuses on quadrilaterals, specifically defining squares as quadrilaterals with four equal sides forming right angles. The document provides formulas for calculating the perimeter of a square when given the length of a side or vice versa. It includes examples of calculating perimeter when given side length or when given total perimeter. It emphasizes perimeter as the total distance around a closed shape and provides real-life examples of measuring perimeter.
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NCV 3 Mathematical Literacy Hands-On Support Slide Show - Module 4
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samle
The document discusses several topics related to mobile multiplayer games including:
- The speaker's background with concepts like frag, power-up, and sprites in first-person shooter games.
- How elements of multiplayer games like asynchronous system and group management are important for mobile games.
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Geometry
- 1. Geometry Exploring Area and Perimeter
- 15. P = 4s A = s 2
- 16. THE END