Perimeter & Area 5.1

• Define perimeter and area.

• Find the perimeter of a figure.

• Use two methods to find the area of compound figures.

• Apply the area and formula of a rectangle and triangle.

• Approximate the area of an irregular figure.

• Apply area to real world situations.

AreaArea• The number of square units needed to cover the

region inside a figure.

• Area is always measured in square units!

There are 40 squares covering the inside

of the figure.

AreaArea• To calculate the area of a rectangle use

the formula: Area = Length x Width

Area = 9m x 2mArea = 18 square meters

AreaArea• To calculate the area of a triangle use the

formula: Area = ½ Base x Height

PerimeterPerimeter• The perimeter is the distance around a figure.

StartStart at one of the vertices and sum the numbers clockwise or counterclockwise.

10 + 6 + 4 + 10 + 10 + 6 + 4 + 10 = 60 m

Find the Area & PerimeterFind the Area & Perimeter

perimeter 12 ina. b. c.

5 inches

3 inches

Perimeter = 20 inches

Area = 9 inches²

area 5 in2

perimeter 20 cm

about 9 cm2

perimeter 16 cm

about 7 cm2

This side was 8mbut because you

split it to make tworegular rectangles,

look carefully atevery side of the

figure to see whatthe new measurements

will be!

Don’t forget the rule,opposite sides are

equal!

This will help you find themissing measurements!

Find the area of rectangle “A”

A= L x WA = 4m x 4m

A = 16 square m

Find the area of rectangle “B”

A= L x WA = 10m x 4m

A = 40 square m

40 square m+ 16 square m

56 square m

The total area is 56 square m.

Find the AreaFind the Area

10cm

8cm

8cm

2cm

4cm

4cmArea =4 x 10

40cm2

Area =4 x 8

32cm2

Total area = 40 + 32 = 72 cm2

A shape that is made from other shapes is known as a composite

shape.

To find the area of this shape we

have to split it up into two

rectangles.

AreaArea

9cm

5cm

5cm

2cm

4cm

5cm

4cm

2cm

Area =5 x 9

45cm2

Area =4 x 5

20cm2

Total area = 45 + 20 = 65 cm2

Perimeter = 36 cm

Area & PerimeterArea & Perimeter

6cm

6cm

11cm

2cm

4cm

5cmArea =2 x 5

10cm2 Area =6 x 6

36cm2

Total area = 10 + 36 = 46 cm2

Perimeter = 34 cm

Area & PerimeterArea & Perimeter

11cm

7cm

4cm

3cm 3cm

3cm

7cm

Total area = 28 + 16 + 21 = 65 cm2

Perimeter = 42 cm

Area =4 x 7

Area =4 x 4

4cm

Area =3 x 7

21cm2

28cm2 16cm2

There is another way of doing this

question.

7cm

4cm

3cm 3cm

3cm

7cm

Total area = 77 – 12 = 65 cm2

Perimeter = 42 cm

Area =7 x 11

Area =3 x 4

4cm

77cm2

12cm2

Lost Area MethodLost Area Method

9cm

5cm

5cm

2cm

4cm

5cm

4cm

2cm

Find the area using Find the area using composition of area methodcomposition of area method

A = 5 x 9 + 5 x 4

A = 45 + 20

A = 65 cm2

6cm

6cm

11cm

2cm

4cm

5cm

Find the area using the lost area methodFind the area using the lost area method

A = 6 x 11 – 5 x 4

A = 66 – 20

A = 46 cm2

Find the area of the figure.Find the area of the figure.

Total area = 16(14) – 60 – 60 = 104 m2

Total area=3,560 square ft.

Find the area of the figure.Find the area of the figure.

$64.80

Mike is remodeling his kitchen. The countertop he wants costs $2.70 per square foot. How much will Mike have to spend on his remodeling project?

Total area = 12 + 12 = 24 ft2

Price per square foot $2.70

2.70

x 24

Answer the following question.Answer the following question.

Approximate Area of an Irregular FigureApproximate Area of an Irregular Figure

There are 8 squares completely inside the figure (X) and 12 partly inside the figure (•).

Count the complete squares.

X X

X X

Count the partial squares.

Approximate Area of an Irregular FigureApproximate Area of an Irregular Figure

about 7.5 cm2

Estimate the shaded area. The grid has squares with side lengths of 1 cm.

about 7 cm2a. b.

about 10.5 cm2

Estimate the shaded area. The grid has squares with side lengths of 1 cm.

a.

Find the area of the composite figure that is Find the area of the composite figure that is made up of known shapesmade up of known shapes

Add the area of the rectangle to the Add the area of the rectangle to the

area of the two triangles.area of the two triangles.

bh2

1A

2units9A)3)(6(2

1A

A = l x w

A = 6 x 5 A = 30 units2

2units5.2A)1)(5(2

1A

Total Area = 30 + 2.5 + 9 Total Area = 41.5 units2

4cm

4cm

4cm

6cm

8cm2cm

Find the area.

about 40 cm2 about 24 cm2a. b.

15 x 20 = 300 square units

2(15) + 2(20) = 70 units

3 x 20 = 60 square units

2(3) + (2)20 = 46 units

8 x 13 = 104 square units

Answer each of the following questions.

AssignmentAssignment

5.1A 1 - 8 5.1A 1 - 8 and and

5.1B 1 - 105.1B 1 - 10

Day 2 Basic Area 1 – 29 Day 2 Basic Area 1 – 29