Basic Geometric Properties

Unit 3 Lesson 7 Finding Area of Figures made up of Triangles and

Parallelograms

Reminders

Rectangle

length

Area = length width

widthbase

Triangle

height

Area = ½ base height

Composite shapes

This is a composite shape because it is made up of more than one basic shape

or

Example 1: Find the area of this shape

12 cm

3 cm

8 cm

5 cm

We can split it into 2 rectangles, A and B

A

B

Rectangle A has area 5 8 = 40 cm2For rectangle B, we have to find another length.

x

Rectangle B has area 7 3 = 21 cm2

So total area = 40 + 21 = 61 cm2

40 cm2

Can you see why it is x = 7 cm?

21 cm2

11cm

8 cm

5 cm

x

y

Area x = 8 X 11 =

4cm

Area y = 5 X 4 =

Total Area =

Need to split up

10cm

7 cm

4 cmx

y

Area x =

3cm

Area y =

Total Area =

Find the area

6 cm

5 cm

7 cm

12 cm

A B

CWe can split it into 3 rectangles, A, B and C

X3 cm

Because of the symmetry of the shape, can you see why these two lengths must be 3 cm each?Can you also see why the dotted lines are y = 2 cm each

y

Rectangle AArea =Rectangle B

Rectangle CArea =

Total area =

21cm2 21cm2

12cm2

You Try1.

2.

3. 4.

6cm

4cm

3cm

9cm

3cm

2cm

7cm

5cm

7cm

4cm6cm

3cm 6cm

7cm

4cm2cm

12cm2

6cm2

12cm2

8cm2

9cm

8 cm

4 cm

x

y

Area x =

8 cm 7cm

Area y =

Total Area =

Steps to success Split into small rectangles Calculate any missing lengthsWork out area of each rectangleAdd for total areaRemember units (square!)

Area of Compound Shapes13 cm

8cm

9 cm

3cmx

y

Area x = 8 X 9 = 72 cm2

?4cm

Area y = 3 X 4 = 12cm2

Total Area = 72 + 12

= 84

cm2

14cm

8 cm

10 cmx

y

Area x = 10 X 8 = 80 cm2

4 cm

Area y = ½ X 8 X 4= 16 cm2

Total Area = 80 + 16

= 96cm2

Other Compound Shapes

Area of Composite Shapes Find the area of all three triangles.

Plan:

Area of a Triangle

½(b)(h)

½(24)

6 in

5 in

4 in

12 in

½(6)(4)

One triangle is 12 square inches

Since 3 triangles are the same.

3 x 12 = 36 square inches

3 m

7.5 m

13 m

12.5 m

6. Find the area and perimeter

Area =

Find the area of the arrow.

Area =

10m

3m

7m

1m

Big Area = 3 X 10 = 30m2

White Area = 7 X 1 = 7m2

Green Area = 30 – 7 = 23m2

Find the area of the green only

Practice Problems pages 110 and 111Odd #1 - 13

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