Area

1
AREA of Rectangle, triangle and circle
2
Area of a Rectangle

• LEARNING OBJECTIVE
• To come up with a formula for the area of a
  rectangle
• To use the formula to solve problems.

6 m
Length
2 m
Width
6 x 2 12 m
2
AREA Length x Width
3
Example 1
Solution
Area Length x Width
12 cm
Area 12 x 8
2
Area 96 cm
8 cm

• What is the area of the
• rectangle ?

4
Example 2

• The perimeter of a rectangular pool is 56
  meters. If the length of the pool is 16 meters,
  then find its width.

Solution
The perimeter P of a rectangle is given by the
formula, P  2l  2w , Given that, the
perimeter is 56 meters and the length is 16
meters. So, substitute these values into the
formula. 56 2( 16) 2w Simplify. 56 36 2w
Subtract 32 from both sides. 24 2w Divide each
side by 2. 12  w Therefore, the width of the
rectangular pool is 12 meters.
w
16 m
5
Example 3
Solution

• The area of a rectangular fence is 500 square
  feet. If the width of the fence is 20 feet, then
  find its length.

Area Length x Width
Given that, the area is 500 square feet and the
width is 20 feet. So, substitute these values
into the formula. 500 length x 20 Divide
each side by 20 to isolate length . 25  length
Therefore, the length of the rectangular fence
is 25 feet.
500 ft²
20 ft.
6
Area of a Triangle

• LEARNING OBJECTIVE
• To come up with a formula for the area of a
  triangle.
• To use the formula to solve problems.

Area of rectangle length x width 7 x 4
28 cm
2
4 cm
4 cm
Area of triangle ½ x area of rectangle ½
x 28 14 cm
Height
2
7 cm
7 cm
Base
AREA ½ x Base x Height
7
Example 1
Solution
Area ½ Base x Height
Area ½ x 12 x 8
Area ½ x 96 32 cm
8 cm
2
12 cm

• What is the area of the triangle?

8
Example 2

• find the area of an acute triangle with a base
  of 15 inches and a height of 4 inches.

Solution
Area ½ Base x Height
Area ½ x 15 x 4
Area ½ x 60 30 in
4 inches
2
15 inches
9
Example 3

• The area of the triangle is 18 square feet and
  the base is 3 feet. Find the height.

Solution
Area ½ Base x Height
18 ft² ½ x 3 x H
Multiplying both sides of the equation by 2, we
get 36 ft2  (3 ft)  Dividing both sides of
the equation by 3 ft, we get 12 ft  h The
height of the triangle is 12 ft.
18 ft²
3 ft.
10
Area of a Circle

• LEARNING OBJECTIVE
• To use the area of circle to solve problems.

Find the area of the circle. Solution A pr²
A p(10) ² A 100p cm ²
radius
10 cm
pr²
AREA
11

Example 2
Find the area the circle with a diameter of 10
inches.
Solution Step 1 Write down the formula A
pr2 Step 2 Change diameter to radius r ½ d
½ x 10 5 Step 3 use the formula A p52 
25p Answer The area of the circle is 25p 
78.55 square inches.
10 cm
12

Example 3
A cow is tied to a post in the field.  If the
length of the rope is 45 feet, what is the area
of the field in which the cow can graze?
Solution The rope acts just like a radius in
this problem r 45 A p r2 A p(45)2 A
2,025p The sheep grazes in an area
2,025psquare feet.
45 ft