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
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
CONTENTS
DEFINITION CIRCLE TRIANGLE SQUARE RECTANGLE SECTOR
DEFINITION OF AREA
• The extent or measurement of a surface or piece • Its units are meter square(m^2) in SI(system international) Units, feet square(ft^2) in F.P.S(foot pound second) or British system and centimeter square(cm^2) in C.G.S(centimeter gram second) or French System. • Simplest formula to measure area is Area=Width*Length
CIRCLE
A ROUND PLANE FIGURE WHOSE BOUNDARY (THE CIRCUMFERENCE) CONSISTS OF POINTS EQUIDISTANT FROM A FIXED POINT (THE CENTRE).
MEASUREMENT OF THE AREA OF CIRCLE
RADIUS (R)
A straight line from the centre to the circumference of a circle or sphere. How to Measure Area Practically WE just simply need to find the radius by using scale and then use this formula
TRIANGLE
A PLANE FIGURE WITH THREE STRAIGHT SIDES AND THREE ANGLES.
MEASUREMENT OF THE AREA OF TRIANGLE
HOW TO FIND AREA OF TRIANGLE PRACTICALLY
• We just simply need to use scale and then measure the height and base of the triangle
SQUARE
A PLANE FIGURE WITH FOUR EQUAL STRAIGHT SIDES AND FOUR RIGHT ANGLES.
MEASUREMENT OF THE AREA OF SQUARE
HOW TO FIND AREA OF SQUARE PRACTICALLY
• We just simply need to use scale and measure the length of one of four sides
RECTANGLE
A PLANE FIGURE WITH FOUR STRAIGHT SIDES AND FOUR RIGHT ANGLES, ESPECIALLY ONE WITH UNEQUAL ADJACENT SIDES, IN CONTRAST TO A SQUARE.
MEASUREMENT OF THE AREA OF RECTANGLE
HOW TO FIND AREA OF RECTANGLE PRACTICALLY
• We just simply need to use scale and measure the length and width of the rectangle
SECTOR
THE PLANE FIGURE ENCLOSED BY TWO RADII OF A CIRCLE OR ELLIPSE AND THE ARC BETWEEN THEM.
MEASUREMENT OF THE AREA OF SECTOR
HOW TO FIND AREA OF SECTOR PRACTICALLY
• We just simply need to use scale and measure the length and width of the rectangle
GEOMETRY SCALES USED FOR THE ABOVE SHAPES
GEOMETRY SCALES USED FOR THE ABOVE SHAPES
SIGNIFICANCE OF MEASUREMENT OF AREA Everything which exists has a specific mass and area which we need to measure for various reasons, some of these are described here: • We use measurement of area in different aspects of life specially when are dealing with standards of different objects , area , is one the first things, which comes in our mind. i.e. standard for property is area(how large property is) and
SIGNIFICANCE OF MEASUREMENT OF AREA
similarly when we need to buy cloth we use area as an standard and pay price according to the area of that piece of cloth. • Engineering and its related fields are impossible to exist without the measurement of area. i.e. we need machines and reactors of different areas while working in a chemical plant for specific uses.
SIGNIFICANCE OF MEASUREMENT OF AREA
• Measurement of area plays an important role in architecture and designing. Whenever we need to build an object again area is
CONTENTS
DEFINITION CIRCLE TRIANGLE SQUARE RECTANGLE SECTOR
DEFINITION OF AREA
• The extent or measurement of a surface or piece • Its units are meter square(m^2) in SI(system international) Units, feet square(ft^2) in F.P.S(foot pound second) or British system and centimeter square(cm^2) in C.G.S(centimeter gram second) or French System. • Simplest formula to measure area is Area=Width*Length
CIRCLE
A ROUND PLANE FIGURE WHOSE BOUNDARY (THE CIRCUMFERENCE) CONSISTS OF POINTS EQUIDISTANT FROM A FIXED POINT (THE CENTRE).
MEASUREMENT OF THE AREA OF CIRCLE
RADIUS (R)
A straight line from the centre to the circumference of a circle or sphere. How to Measure Area Practically WE just simply need to find the radius by using scale and then use this formula
TRIANGLE
A PLANE FIGURE WITH THREE STRAIGHT SIDES AND THREE ANGLES.
MEASUREMENT OF THE AREA OF TRIANGLE
HOW TO FIND AREA OF TRIANGLE PRACTICALLY
• We just simply need to use scale and then measure the height and base of the triangle
SQUARE
A PLANE FIGURE WITH FOUR EQUAL STRAIGHT SIDES AND FOUR RIGHT ANGLES.
MEASUREMENT OF THE AREA OF SQUARE
HOW TO FIND AREA OF SQUARE PRACTICALLY
• We just simply need to use scale and measure the length of one of four sides
RECTANGLE
A PLANE FIGURE WITH FOUR STRAIGHT SIDES AND FOUR RIGHT ANGLES, ESPECIALLY ONE WITH UNEQUAL ADJACENT SIDES, IN CONTRAST TO A SQUARE.
MEASUREMENT OF THE AREA OF RECTANGLE
HOW TO FIND AREA OF RECTANGLE PRACTICALLY
• We just simply need to use scale and measure the length and width of the rectangle
SECTOR
THE PLANE FIGURE ENCLOSED BY TWO RADII OF A CIRCLE OR ELLIPSE AND THE ARC BETWEEN THEM.
MEASUREMENT OF THE AREA OF SECTOR
HOW TO FIND AREA OF SECTOR PRACTICALLY
• We just simply need to use scale and measure the length and width of the rectangle
GEOMETRY SCALES USED FOR THE ABOVE SHAPES
GEOMETRY SCALES USED FOR THE ABOVE SHAPES
SIGNIFICANCE OF MEASUREMENT OF AREA Everything which exists has a specific mass and area which we need to measure for various reasons, some of these are described here: • We use measurement of area in different aspects of life specially when are dealing with standards of different objects , area , is one the first things, which comes in our mind. i.e. standard for property is area(how large property is) and
SIGNIFICANCE OF MEASUREMENT OF AREA
similarly when we need to buy cloth we use area as an standard and pay price according to the area of that piece of cloth. • Engineering and its related fields are impossible to exist without the measurement of area. i.e. we need machines and reactors of different areas while working in a chemical plant for specific uses.
SIGNIFICANCE OF MEASUREMENT OF AREA
• Measurement of area plays an important role in architecture and designing. Whenever we need to build an object again area is
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Step 1: Make sure the bottom numbers (the denominators) are the same
Step 2: Add the top numbers (the numerators), put that answer over the denominator
Step 3: Simplify the fraction (if possible)
Step 1. Make sure the bottom numbers (the denominators) are the same
Step 2. Subtract the top numbers (the numerators). Put the answer over the same denominator.
Step 3. Simplify the fraction (if needed).
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2. Polygons
• A polygon is a plane shape with straight sides.
Polygons are 2-dimensional shapes. They are made of
straight lines, and the shape is "closed" (all the lines
connect up).
6. Perimeter
The perimeter of a two-dimensional shape is the distance around the shape. You
can think of wrapping a string around a triangle. The length of this string would be
the perimeter of the triangle. Or walking around the outside of a park, you walk the
distance of the park’s perimeter.
Some people find it useful to think “Perimeter” because the edge of an object is its
rim and peRIMeter has the word “rim” in it.
rim
7. Perimeter
If the shape is a polygon, then you can add up all the lengths of the sides
to find the perimeter.
Be careful to make sure that all the lengths are measured in the same
units. You measure perimeter in linear units, which is one dimensional.
Examples of units of measure for length are inches, centimeters, or
feet.
8. Perimeter examples
Find the perimeter of the given regular polygon. All
measurements indicated are centimetres.
Perimeter = S +S + S +S
PeRIMeter = 3cm +3cm+ 3cm + 3cm.
P=12cm
Since all the sides are measured in
centimeter, just add the lengths of all
four sides to get the perimeter.
Remember to include units.
9. Perimeter examples
Find the perimeter of the given non-regular
polygon. All measurements indicated are
centimetres.
Perimeter = S +S + S +S
PeRIMeter = 5cm +3cm+ 5cm + 3cm.
P=16cm
Since all the sides are measured in
centimetres, just add the lengths of all
four sides to get the perimeter.
Remember to include units.
10. Perimeter examples
Find the perimeter of the given non-regular
polygon. All measurements indicated are inches.
Perimeter = S +S + S +S+ S +S.
PeRIMeter = 5 +3 + 6 + 2 + 3 + 3.
P = 22 inches
Since all the sides are measured in inches,
just add the lengths of all six sides to get
the perimeter.
Remember to include units.
11. Perimeter examples
Find the perimeter of the given non-regular
polygon. All measurements indicated are feet.
Perimeter = S +S + S +S
PeRIMeter = 8 +10 + 8 + 14.
P = 40 feet
Since all the sides are measured in feet,
just add the lengths of all four sides to
get the perimeter.
Remember to include units.
12. AreaThe area of a two-dimensional figure describes the amount of surface
the shape covers.
You measure area in square units of a fixed size.
Examples of square units of measure are square inches, square
centimeters, or square miles.
When finding the area of a polygon, you count how many squares of a
certain size will cover the region inside the polygon.
13. AreaYou can count that there are 16 squares, so the area is
16 square units. Counting out 16 squares doesn’t take too
long, but what about finding the area if this is a larger
square or the units are smaller? It could take a long
time to count.
Fortunately, you can use multiplication. Since there are 4 rows of 4
squares, you can multiply 4 • 4 to get 16 squares! And this can be
generalized to a formula for finding the area of a square with any
length, Area = s x s = s2.
You can write “in2” for square inches and “ft2” for
square feet.
14. AreaTo help you find the area of the many different
categories of polygons, mathematicians have developed
formulas. These formulas help you find the
measurement more quickly than by simply counting.
The formulas you are going to look at are all developed
from the understanding that you are counting the
number of square units inside the polygon. Let’s look at
a rectangle.
15. AreaYou can count the squares individually, but it is much easier to multiply 3
times 5 to find the number more quickly. And, more generally, the area
of any rectangle can be found by multiplying length times width.
Area = L x W = ______2.15 cm
16. Area examples
A rectangle has a length of 8 centimeters and a
width of 3 centimeters. Find the area.
You can count that there are 24 squares,
so the area is 24 square units.
Area = S x S or Area = L x W
Area = 8 x 3
There are 3 rows of 8 squares, you can
multiply 3 • 8 to get 24 squares.
Remember to include units.
It would take 24 squares, each measuring 1 cm
on a side, to cover this rectangle.
17. Area examples
A rectangle has a length of 12 centimeters and a
width of 2 centimeters. Find the area.
You can count that there are 24 squares, so the area is 24 square
units.
It would take 24 squares, each measuring 1 cm on a side, to cover this rectangle.
18. Area examples
Find the area of the rectangles.
Area = L x W
Area = 4 x 2
Area = L x W
Area = 2 x 4
or Area = S x S