Geometry Composite Figures

CONFIDENTIAL 1

Geometry

Composite Figures

CONFIDENTIAL 2

Warm up

Find the area of each regular polygon. Round to the nearest tenth:

1) An equilateral triangle with a side length of 3 cm.

2) A regular hexagon with an apothem of 4√3 m.

CONFIDENTIAL 3

A composite figure is made up of simple shapes such as triangles, rectangles,

trapezoids and circles. To find the area of a composite figure, find the areas of the simple

shapes and then use the Area Addition Postulate.

Composite Figures

CONFIDENTIAL 4

Divide the figure into rectangles.

Area of top rectangle:A = bh = 12(15) = 180 cm2

Area of bottom rectangle:A = bh = 9(27) = 243 cm2

Shaded area:180 cm2 + 243 cm2 = 423 cm2

Finding the area of Composite Figures by Adding

15 cm

12

cm

21

cm

27 cm

15 cm

12

cm12 cm

27 cm9 cm

A) Find the area of the shaded region.

CONFIDENTIAL 5

Divide the figure into parts.

The base of the triangle is :√(10.22 - 4.82) = 9 ft

Area of triangle:A = 1bh = 1(9)(4.8) = 21.6 ft2

2 2Area of rectangle:A = bh = 9(3) = 27 ft2

Area of half circle:A = 1∏r2 = 1∏(4.52) = 10.125∏ ft2

2 2Shaded area:21.6 + 27 + 10.125∏ ≈ 80.4 ft2

Finding the area of Composite Figures by Adding

B)

10.2 ft

7.8 ft

3 ft

10.2 ft

7.8 ft

3 ft

4.5 ft

CONFIDENTIAL 6

Now you try!

1) Find the area of the given figure. Round to the nearest tenth.

37.5 m

22.5 m

75 m

62.5 m

CONFIDENTIAL 7

Sometimes you need to subtract to find the area of composite figures.

CONFIDENTIAL 8

Finding the area of Composite Figures by Subtracting

Subtract the area of the triangle from the area of the rectangle.

Area of top rectangle:A = bh = 18(36) = 648 m2

Area of triangle:A = 1bh = 1(36)(9) = 162 m2

2 2

Area of the figure:A = 648 – 162 = 486 m2

A) Find the area of the shaded region.

9 m

18 m

36 m

CONFIDENTIAL 9

The two half circles have the same area as one circle. Subtract the area of the circle from the area of the rectangle.

Area of top rectangle:A = bh = 33(16) = 528 ft2

Area of circle:A = ∏r2 = ∏(82) = 64∏ ft2

Area of the figure:A = 528 – 64∏ = 326.9 ft2

B) Find the area of the shaded region.

16 ft

33 ft

CONFIDENTIAL 10

Now you try!

2) Find the area of the shaded region. Round to the nearest tenth.

6 in

CONFIDENTIAL 11

Katie is using the given plan to convert part of her lawn to a xeriscape garden. A newly planted xeriscope uses 17 gallons of water per square foot per year. How much water will the

garden require in one year?

12 ft

28.5 ft

10.5 ft7

.5 f

t

6 f

t

18 ft

19

.5 ft

12 ft

28.5 ft

10.5 ft

7.5

ft

6 f

t

18 ft

19

.5 ft

Divide the garden into parts.Area of top rectangle:A = bh = 28.5(7.5) = 213.75 ft2

Area of center trapezoid:A = 1(12 + 18)(6) = 90 ft2

2Area of bottom rectangle:A = bh = 12(6) = 72 ft2

Area of the garden is:213.75 + 90 + 72 = 375.75 ft2

The garden will use (375.75)(17) = 6387.75 gallons of water per year

CONFIDENTIAL 12

Now you try!

3) The lawn that Katie is replacing requires 79 gallons of water per square foot per year. How much water will

Katie save by planting the xeriscape garden?

12 ft

28.5 ft

10.5 ft

7.5

ft

6 f

t18 ft

19

.5 ft

CONFIDENTIAL 13

To estimate the area of an irregular shape, you can sometimes use a composite figure. First draw a composite figure that resembles the irregular shape. Then divide the composite

figure into simple shapes.

CONFIDENTIAL 14

Estimating areas of irregular shapesUse a composite figure to estimate the shaded area. The grid

gas squares with side length of 1 cm.

Draw a composite figure that approximates the irregular shape. Find the area of each part of the

composite figure.

a

b

c

d

Area of triangle, a:

A = 1bh = 1(3)(1) = 1.5 cm2

2 2

Area of Parallelogram, b:

A = bh = 3(1) = 3 cm2

CONFIDENTIAL 15

Area of trapezoid, c:

A = 1(3 + 2)(1) = 2.5 cm2

2

Area of triangle, d:

A = 1bh = 1(2)(1) = 1 cm2

2 2

Area of composite figure:1.5 + 3 + 2.5 + 1 = 8 cm2

a

b

c

d

The shaded area is about 375.75 ft2

CONFIDENTIAL 16

Now you try!

4) Use a composite figure to estimate the shaded area. The grid gas squares with side length of 1 ft.

CONFIDENTIAL 17

Now some problems for you to practice !

CONFIDENTIAL 18

Find the area of the shaded region. Round to the nearest tenth:

Assessment

1)

2)4

cm

12 cm

5 cm 3 cm 2 cm

4 ft

5 f

t

CONFIDENTIAL 19

3)

4)

8 in

.

18 in.

3 in.

3 m 2 m

6 m

5 m

CONFIDENTIAL 20

5)

Find the area of the shaded region. Round to the nearest tenth:

12 ft

4 ft

12 ft

16 ft6)

12 cm

12

cm

12 cm

CONFIDENTIAL 21

7) Shelby is planting grass in an irregularly shaped garden as shown The grid has squares of side 1 yd. Estimate the area of the garden. Given that grass cost $6.50 per square yard, find the cost of the grass.

CONFIDENTIAL 22

A composite figure is made up of simple shapes such as triangles, rectangles,

trapezoids and circles. To find the area of a composite figure, find the areas of the simple

shapes and then use the Area Addition Postulate.

Composite Figures

Let’s review

CONFIDENTIAL 23

Divide the figure into rectangles.

Area of top rectangle:A = bh = 12(15) = 180 cm2

Area of bottom rectangle:A = bh = 9(27) = 243 cm2

Shaded area:180 cm2 + 243 cm2 = 423 cm2

Finding the area of Composite Figures by Adding

15 cm

12

cm

21

cm

27 cm

15 cm

12

cm12 cm

27 cm9 cm

A) Find the area of the shaded region.

CONFIDENTIAL 24

The two half circles have the same area as one circle. Subtract the area of the circle from the area of the rectangle.

Area of top rectangle:A = bh = 33(16) = 528 ft2

Area of circle:A = ∏r2 = ∏(82) = 64∏ ft2

Area of the figure:A = 528 – 64∏ = 326.9 ft2

B) Find the area of the shaded region.

16 ft

33 ft

CONFIDENTIAL 25

Katie is using the given plan to convert part of her lawn to a xeriscape garden. A newly planted xeriscope uses 17 gallons of water per square foot per year. How much water will the

garden require in one year?

12 ft

28.5 ft

10.5 ft7

.5 f

t

6 f

t

18 ft

19

.5 ft

12 ft

28.5 ft

10.5 ft

7.5

ft

6 f

t

18 ft

19

.5 ft

Divide the garden into parts.Area of top rectangle:A = bh = 28.5(7.5) = 213.75 ft2

Area of center trapezoid:A = 1(12 + 18)(6) = 90 ft2

2Area of bottom rectangle:A = bh = 12(6) = 72 ft2

Area of the garden is:213.75 + 90 + 72 = 375.75 ft2

The garden will use (375.75)(17) = 6387.75 gallons of water per year

CONFIDENTIAL 26

Estimating areas of irregular shapesUse a composite figure to estimate the shaded area. The grid

gas squares with side length of 1 cm.

Draw a composite figure that approximates the irregular shape. Find the area of each part of the

composite figure.

a

b

c

d

Area of triangle, a:

A = 1bh = 1(3)(1) = 1.5 cm2

2 2

Area of Parallelogram, b:

A = bh = 3(1) = 3 cm2

CONFIDENTIAL 27

Area of trapezoid, c:

A = 1(3 + 2)(1) = 2.5 cm2

2

Area of triangle, d:

A = 1bh = 1(2)(1) = 1 cm2

2 2

Area of composite figure:1.5 + 3 + 2.5 + 1 = 8 cm2

a

b

c

d

The shaded area is about 375.75 ft2

CONFIDENTIAL 28

You did a You did a great great job today!job today!