1. Area and Perimeter

2. What Is Area ? Area is the amount of space inside a shape: Area Area
1cm
Area is measured in square units
1cm2
A square centimeter is a square measuring one centimeter in each direction.
It can be written as :

3. Area of a Rectangle and Square
Area = Length · Width
A = bh

4. Example 1
Find the area of the shapes below :
(1)
8cm
6cm
4.2m
2.7m
(2)
(3)
17cm
8cm
12cm
5cm
Purple = 48 cm2
Yellow = m2
Green = 141 cm2

5. Area of a Parallelogram and Rhombus
Area = Base · Height
A = bh
A = 60 cm2

6. The Area Of A Triangle. A = ½ BH Area = ½ x Base x Height
Consider the right angled triangle below:
8 cm
5cm
What is the area of the triangle ?
Area = ½ x 40 = 20cm2
Base
Height
Of what shape is the triangle half?
Rectangle
Formula for Area of a Triangle is:
What is the area of the rectangle?
Area = ½ x Base x Height
Area = 8 x 5 = 40 cm2
A = ½ BH

7. Calculate the area of the triangles below:
10cm
6cm
6.4m
3.2m
Red = 30 cm2
Yellow = cm2

8. Calculate the area of the triangle below:

9. Area of a Trapezoid
Area = ½ h ( b1 + b2 )
(b1)
(b2)

10. Calculate the area of the trapezoid below :
16cm
11cm
13cm
( )(1/2 x 13) = cm2

11. Area = ½ h ( b1 + b2 ) Find the Area of Trapezoid EFGH
(4+6)(1/2 x 4) = 20

12. RADIUS
The radius is the distance from the center of a circle to any point on a circle.

13. DIAMETERS

14. We use Pi as the measurement to help us find the circumference and area of a circle.
Pi, not Pie!

15. HINT: Pi =3.14

16. Two formulas are used in finding the circumference of a circle.
Circumference = d
4in
3.14 x 4in.
12.6in.

17. When the radius of a circle is given, the following formula should be used.
Circumference = 2 r
2 x 3.14 x 5cm
31.4cm
5 cm ∙

18. Area of a Circle
Area = r2
4in
3.14 x 2 x 2
12.56in2

19. Area of a Circle
Area = r2
3.14 x 5 x 5
78.5cm2
5 cm ∙

20. Change in Dimension Polygons
If you change dimensions by a and b
then
Area changes a x b

21. Change in Dimensions Circles
If you change the radius by c then Area changes by c2

22. John and Mary each have a garden, in the shape of a square
John and Mary each have a garden, in the shape of a square. If the area of John’s garden is four times the area of Mary’s garden, how do the perimeters of the two gardens compare?
The perimeter of Johns garden is twice the perimeter of Mary’s garden. Width and Length are both doubled.

23. Jenni made a small table for a class project
Jenni made a small table for a class project. The top of the table is triangular. Her mother wants her to make a larger table. If she changes the dimensions so that both the base and the height of the triangle are tripled, how will the area of the tabletop change?
The area will be 9 times larger.

24. Paula and Munos each made a rectangular garden
Paula and Munos each made a rectangular garden. Paula’s garden is half the length of Munos’. How do the areas of the gardens compare if the gardens have the same width?
The area of Paula’s garden is half the area of Munos’ garden OR The area of Munos’ garden is twice the area of Paula’s garden.

25. Martha made a circular quilt with a radius that is double that of the pattern. How does the area of her quilt compare to that of the pattern?
The area of the quilt is 4 times the area of the pattern. (22 is 4)

26. Jack has his dog secured at a stake with a 5 foot chain
Jack has his dog secured at a stake with a 5 foot chain. If he wants to give his dog nine times the area that he currently has, what length chain should he use?
Jack will need to multiply the chain length (radius) by 3 to multiply the area by 9 (32)

27. A rectangular bathroom has dimensions of
4 ¾ ft by 4 ½ ft.
The floor is made of tiles with side length of 1 foot. What is the number of tiles that will cover the bathroom floor?
You will need tiles.

28. The area of a square is 144. What are the length of the sides?12
The circumference of a circle is 36 inches. What is the radius?
36 ÷ 3.14 = = diameter
÷ 2 = = radius