1. Lesson #2: Perimeter & Area of Shapes
Unit 3: Geometry
Lesson #2: Perimeter & Area of Shapes

2. The Perimeter Of A Shape.
Regular Octagon
6cm
4cm
5cm
3cm

3. The Idea Of Perimeter.
Perimeter is the distance around the outside of a shape.
What is the perimeter of the shapes below ?
(2)
5.6m
8.9m
(1)
6cm
4cm
P =
6 +
4 +
6 + 4
P =
2 x
( )
P =
20cm
P = 29m

4. (3)
5cm
3cm
4cm
(4)
10m
Regular Octagon
P =
3 +
4 + 5
P =
12cm
P =
8 x 10
P =
80 m

5. What Goes In The Box ? Calculate the perimeter of the shapes below:
(2)
9.7cm
11.4cm
(1)
9 cm
4cm
P = 26cm
P=32.5cm
(3)
7.8 m
10.3m
8.1m
7.9m
(4)
12cm
P = 34.1m
P=72cm

6. The Perimeter Of A Circle.
Look at the circle below:
Circumference.
What do we call the distance around the circle?
What do we call the distance across the circle ?
Diameter
Key Question.
How many times bigger is the diameter of the circle compared to the diameter ?
The circumference is a bit more than three times the diameter.

7. Estimating The Circumference.
If we know that the circumference of a circle is roughly three times the diameter , then estimate the circumference of the circles below:
(2) 9m
(1)
6cm
Circumference = 3 x diameter
C = 3 x
6cm
Circumference = 3 x diameter
C = 3 x 9m
C = 18 cm
C = 27m

8. The Number Called Pi.
After a great deal of measuring and calculating , Greek mathematicians came up with a better estimate of how many times bigger the circumference was compared to the diameter.
Key Fact.
They found that the circumference was 3.14 times bigger than the diameter. They called 3.14 Pi after a letter in the Greek alphabet. The letter pi is written as :
The Circumference Of A Circle.
Circumference = Pi x Diameter

9. Calculating The Circumference.
Calculate the circumference of the circles below:
(2)
2.8cm
(1)
10m
C =  x D
C =  x D
= 3.14
D = 10m
= 3.14
D = 2.8cm
C = 3.14 x 10
C = 3.14 x 2.8
C = 31.4m
C = 8.8cm

10. What Goes In The Box 2 ?
Calculate the circumference of the circles shown below:
(1)
4cm
(2)
26cm
12.6cm
(3)
2.3m
81.64m
14.4m

11. Perimeter Of More Complex Shapes.
Calculate the perimeter of the shapes below:
(1)
12m
P = D + ( D) 2
P = 12 + (3.14 x12) 2
P =
P = cm

12. (2)
10 m
8 m
P =
10 +
16 +
(3.14 x10 2)
P =
26 +
15.7
P = 41.7m

13. (3)
10cm
P =
10 +
10 +
(3.14 x 20) x 0.75
P =
20 +
47.1
P =
67.1 cm

14. Perimeter
Perimeter is the distance around the outside edge of a flat object.
Perimeter is reported as a total number of linear units.

15. When you measure the amount of wallpaper border to go around a room, you measure it in lengths.?
Would the perimeter of your bedroom or the perimeter of your house be greater? ?
You’re right! The perimeter of your house is greater than the perimeter of your bedroom.

16. Let’s find the perimeter of this surface if each square is equal to one cm
Count the number of sides.
Perimeter = 24 cm

17. The perimeter is equal to 12.
Try this one!
Count the number of sides to determine the perimeter of this flat object.
The perimeter is equal to 12.

18. Let’s do these problems together.
Two neighbors build swimming pools. This is what the pools look like.
Which family has the pool with the bigger swimming area?
Family B
Family A

19. The area of Family A’s pool is?
8 square units.
The area of Family B’s pool is?
7 square units
Therefore, Family A has the pool with
the bigger swimming area.
Family B
Family A

20. The perimeter of Family A’s pool is 12 units long.
Now look at those same two pools. Which family has more side panels of the pool to clean?
The perimeter of Family A’s pool is 12 units long.
The perimeter of Family B’s pool is 14 units long.
Therefore, Family B has more side panels of the pool to clean.
Family B
Family A

21. Area
Area is the amount of surface space that a flat object has.
Area is reported in the amount of square units.

22. When you measure the amount of carpet to cover the floor of a room, you measure it in square units.?
Would the area of your bedroom or the area of your house be greater? ?
You’re right! The area of your house is greater than the area of your bedroom.

23. Lets find the area of this surface if each square is equal to one foot.
Count the number of squares. 1 2
Area = 15 cm² 3 4 5 6 7 8 9 10 11 12 13 14 15

24. The area is equal to 9 square units.
Try this one!
Count the number of green squares to determine the area of this surface. What is the area? 1 2 3 4 5 6 7 8 9
The area is equal to 9 square units.

25. Area of a Rectangle
The number of square units needed to cover the surface of a figure.
The formula is: A = L x W
Area is measured in square units.
9 cm
A = L x W
A = 14 cm x 9 cm
A = 126 cm²
14 cm

26. Area of a Square
The number of square units needed to cover the surface of a figure.
The formula is: A = s² or A = s x s
Area is measured in square units.
A = s² A = s x s
A = 6 cm² A = 6 cm x 6 cm.
A = 36 cm²
6 cm.

27. Area of a Triangle
The number of square units needed to cover the surface of a figure.
The formula is: A =½bh or A = bh 2
Area is measured in square units.
A =½bh
A = ½(5 in. x 4 in.)
A = ½ (20 sq. in.)
A = 10 cm2 .
5 cm
5 cm
4 cm.
5 cm

28. Area of Circles
The formula for the area of circles is a bit more complicated than the others.
area = pi x radius squared
If a circle has a radius of 8 cm, what is its area?
A = 3.14 x 8^2
A = cm2
A = πr2

29. We have learned many formulas for finding the perimeter and area of various objects such as rectangles, squares, triangles, and circles.
We have learned that perimeter concerns how much is needed to surround an object and that area is how much is needed to cover an object.
Summary

30. Calculating Areas Rectangle Parallelogram Square Triangle Trapezoid r
Circle