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This pdf includes the following topics:-

Definition and Strategy

Examples

Applications

Definition and Strategy

Examples

Applications

1.
Notes: Area of Composite Figures

2.
I. Definition and Strategy

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 add them together.

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 add them together.

3.
II. Examples

Ex 1a: Find the shaded area. Round to the

nearest tenth, if necessary.

Divide the figure into parts.

area of half circle:

area of triangle:

area of the rectangle: A = bh = 20(14) = 280 mm2

shaded area: 50 + 280 + 84 ≈ 521.1 mm2

Ex 1a: Find the shaded area. Round to the

nearest tenth, if necessary.

Divide the figure into parts.

area of half circle:

area of triangle:

area of the rectangle: A = bh = 20(14) = 280 mm2

shaded area: 50 + 280 + 84 ≈ 521.1 mm2

4.
Ex 1b: Find the shaded area. Round to the

nearest tenth, if necessary.

Divide the figure into parts.

area of parallelogram:

A = bh = 8(5)= 40ft2

area of triangle:

shaded area: 40 + 25 = 65 ft2

nearest tenth, if necessary.

Divide the figure into parts.

area of parallelogram:

A = bh = 8(5)= 40ft2

area of triangle:

shaded area: 40 + 25 = 65 ft2

5.
Ex 1c: Find the shaded area. Round to the

nearest tenth, if necessary.

Area of rectangle:

A = bh = 37.5(22.5)

= 843.75 m2

Area of triangle:

Total shaded area is

about 1781.3 m2.

= 937.5 m2

nearest tenth, if necessary.

Area of rectangle:

A = bh = 37.5(22.5)

= 843.75 m2

Area of triangle:

Total shaded area is

about 1781.3 m2.

= 937.5 m2

6.
III. Examples with Subtraction

Sometimes you might need to subtract a figure.

Ex 2a: Find the shaded area. Round to the nearest

tenth, if necessary.

area of a triangle:

area of the half circle:

Subtract the area of the area of figure:

half circle from the area

234 – 10.125 ≈ 202.2 ft2

of the triangle.

Sometimes you might need to subtract a figure.

Ex 2a: Find the shaded area. Round to the nearest

tenth, if necessary.

area of a triangle:

area of the half circle:

Subtract the area of the area of figure:

half circle from the area

234 – 10.125 ≈ 202.2 ft2

of the triangle.

7.
Ex 2b: Find the shaded area. Round to the

nearest tenth, if necessary.

area of circle:

A = r2 = (10)2 = 100 cm2

area of trapezoid:

area of figure: 100 –128 186.2 cm2

nearest tenth, if necessary.

area of circle:

A = r2 = (10)2 = 100 cm2

area of trapezoid:

area of figure: 100 –128 186.2 cm2

8.
Ex 2c: Find the shaded area. Round to the

nearest tenth, if necessary.

area of circle:

A = r2 = (3)2 28.3 in2

area of square:

A = bh (4.24)(4.24) 18 in2

area of figure: 28.3 – 18 = 10.3 in2

nearest tenth, if necessary.

area of circle:

A = r2 = (3)2 28.3 in2

area of square:

A = bh (4.24)(4.24) 18 in2

area of figure: 28.3 – 18 = 10.3 in2

9.
IV. Applications

Ex 3a: A company receives an order for 65 pieces of fabric in

the given shape. Each piece is to be dyed red. To dye 6 in2 of

fabric, 2 oz of dye is needed. How much dye is needed for the

entire order?

To find the area of the shape in square

inches, divide the shape into parts.

The two half circles have the same area as

one circle.

The area of the circle is (1.5)2 = 2.25 in2.

The area of the square is (3)2 = 9 in2.

The total area of the shape is 2.25 + 9 ≈ 16.1 in2.

The total area of the 65 pieces is 65(16.1) ≈ 1044.5 in2.

The company will need 1044.5 ≈ 348 oz of dye

for the entire order.

Ex 3a: A company receives an order for 65 pieces of fabric in

the given shape. Each piece is to be dyed red. To dye 6 in2 of

fabric, 2 oz of dye is needed. How much dye is needed for the

entire order?

To find the area of the shape in square

inches, divide the shape into parts.

The two half circles have the same area as

one circle.

The area of the circle is (1.5)2 = 2.25 in2.

The area of the square is (3)2 = 9 in2.

The total area of the shape is 2.25 + 9 ≈ 16.1 in2.

The total area of the 65 pieces is 65(16.1) ≈ 1044.5 in2.

The company will need 1044.5 ≈ 348 oz of dye

for the entire order.

10.
Ex 3b: The lawn that Katie is replacing requires 79 gallons

of water per square foot per year. She wants to replace the

lawn with a xeriscape garden, which only uses 17 gallons of

water per square foot per year. How much water will Katie

save, per year, by planting a xeriscape garden?

Find the area of the figure.

Area of large rectangle = bh =

7.5(28.5) = 213.75 ft2

(𝑏1 +𝑏2 )ℎ 12+18 6

Area of trapezoid= = =90 ft2

2 2

Area of small rectangle = bh = 6(12)= 72 ft2

Area of garden = 213.75+90+72=375.75 ft2

Area times gallons of water 375.75(79) = 29,684.25

Subtract water used

29,684.25 – 6,387.75 = 23,296.5 gallons saved.

of water per square foot per year. She wants to replace the

lawn with a xeriscape garden, which only uses 17 gallons of

water per square foot per year. How much water will Katie

save, per year, by planting a xeriscape garden?

Find the area of the figure.

Area of large rectangle = bh =

7.5(28.5) = 213.75 ft2

(𝑏1 +𝑏2 )ℎ 12+18 6

Area of trapezoid= = =90 ft2

2 2

Area of small rectangle = bh = 6(12)= 72 ft2

Area of garden = 213.75+90+72=375.75 ft2

Area times gallons of water 375.75(79) = 29,684.25

Subtract water used

29,684.25 – 6,387.75 = 23,296.5 gallons saved.