Unit 3: GeometryLesson #2: Perimeter & Area of Shapes

The Perimeter Of A Shape.

10m

Regular Octagon

6cm

4cm

5cm3cm

4cm

The Idea Of Perimeter.

Perimeter is the distance around the outside of a shape.

What is the perimeter of the shapes below ?

(1)

6cm

4cm

(2)

5.6m

8.9m

P = 6 + 4 + 6 + 4

P = 20cmP = 2 x ( 5.6 + 8.9)

P = 29m

(3)5cm

3cm

4cm

P = 3 + 4 + 5

P = 12cm

(4)

10m

Regular Octagon

P = 8 x 10

P = 80 m

What Goes In The Box ?Calculate the perimeter of the shapes below:

(1)

9 cm

4cm

(2)

9.7cm

11.4cm11.4cm

(3)

7.8 m

10.3m

8.1m 7.9m

(4)

12cm

P = 26cm P=32.5cm

P = 34.1m P=72cm

The Perimeter Of A Circle.Look at the circle below:

What do we call the distance around the circle?

Circumference.

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.

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:

(1)

6cm

Circumference = 3 x diameter

C = 3 x 6cm

C = 18 cm

(2)

9m

Circumference = 3 x diameter

C = 3 x 9m

C = 27m

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 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.

The Circumference Of A Circle.

Circumference = Pi x Diameter

DC

Calculating The Circumference.

(1)

10m

Calculate the circumference of the circles below:

C = x D

= 3.14 D = 10m

C = 3.14 x 10

C = 31.4m

(2)

2.8cm

C = x D

= 3.14 D = 2.8cm

C = 3.14 x 2.8

C = 8.8cm

What Goes In The Box 2 ?Calculate the circumference of the circles shown below:

(1)

4cm

(2)

26cm

(3)

2.3m

12.6cm

81.64m

14.4m

Perimeter Of More Complex Shapes.

Calculate the perimeter of the shapes below:

(1)

12mP = D + ( D)

2

P = 12 + (3.14 x12) 2

P = 12 + 18.84

P = 30.8 cm

(2)

10 m

8 m

P = 10 + 16 + (3.14 x10 2)

P = 26 + 15.7

P = 41.7m

(3)

10cm

P = 10 + 10 + (3.14 x 20) x 0.75

P = 20 + 47.1

P = 67.1 cm

Perimeter is the distance around the outside edge of a flat object.

Perimeter is reported as a total number of linear units.

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.

Perimeter = 24 cm

Let’s find the perimeter of this surface if each square is equal to one cm

Count the number of sides.

Count the number of sides to

determine the

perimeter of this flat object.

The perimeter is equal to

12.

Try this one!

Two neighbors build swimming pools. This is what the pools look like.

Family A

Family B

Which family has the pool with the bigger swimming area?

Let’s do these problems together.

The area of Family A’s pool is?

Family A

Family B

8 square units.

7 square unitsThe area of Family B’s pool is?

Therefore, Family A has the pool with the bigger swimming area.

The perimeter of Family A’s pool is 12 units long.

Family B

Family A

The perimeter of Family B’s pool is 14 units long.

Therefore, Family B has more side panels of the pool to clean.

Now look at those same two pools. Which family has more side panels of the pool to clean?

Area is the amount of surface space that a flat object has.

Area is reported in the amount of square units.

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.

Area = 15 cm²

Lets find the area of this surface if each square is equal to one foot.

Count the number of squares.

1 2

3

4 5 6 7 8

9 10 11 12 13 14

15

Count the number of

green squares to determine

the area of this surface. What

is the area?

The area is equal to 9

square units.

Try this one!

1

5

2

4

7

3

6

8 9

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.

14 cm

9 cmA = L x W

A = 14 cm x 9 cm

A = 126 cm²

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.

6 cm.

A = s² A = s x s

A = 6 cm² A = 6 cm x 6 cm.

A = 36 cm²

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.

5 cm 5 cm

5 cm

4 cm.

A =½bh A = ½(5 in. x 4 in.)A = ½ (20 sq. in.)A = 10 cm2

.

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 = 200.96 cm2

A = πr2

Summary

• 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.

Calculating AreasRectangle

Parallelogram

Square

Triangle

Trapezoid

Circle

b1

b2

r