6th Grade Math Textbook, Fundamentals

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10-9

24 yd

8 yd 10 yd

E

B

D

C

A

24 yd

8 yd 10 yd

Remember:

Area formulas

rectangle: Aw

parallelogram: Abh

triangle: A bh

trapezoid: A (b 1 b 2 )h

circle: Ar^2

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10 cm

8 cm

Area of Complex Figures

Objective To identify polygons and circles within a complex figure •To find or estimate

the area of complex figures involving polygons and circles • To find missing dimensions

in a complex figure given its area

An auditorium has the floor plan shown at the right.
What is the area of the auditorium’s floor?

A is a figure made up of two or more

shapes. You can find the area of a complex figure. Separate

the figure into shapes whose areas you know how to find.

There are two shapes in the complex figure ABCDE.

They are triangle ABEand rectangle BCDE.

Once you’ve identified the different shapes, you can

determine the area of each shape. The area of the complex

figure will be the sum of the areas of the shapes.

complex figure

Find the area of triangleABE:

A bh (10)(8) 40 yd^2

Find the area of rectangleBCDE:

Aw(24)(10) 240 yd^2

Find the sum of the two areas:

Area of the floor Area of triangle Area of rectangle

40 yd^2 240 yd^2 280 yd^2

So the area of the auditorium’s floor is 280 square yards.

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Sometimes the area of a complex figure is calculated by finding

the differenceof the areas of two or more shapes.

What is the area of the shaded figure at the right?

To find the area of the shaded figure, first find the area of the

square and the area of the semicircle. Then subtract the area of

the semicircle from that of the square.

Find the area of the square:

As^2  102 100 cm^2

Find the area of the semicircle:

A (r^2 ) The area of a semicircle is half the area of a circle.

 (3.14 • 4^2 ) Substitute the known value. Use 3.14 for .

25.12 cm^2 Simplify.

Subtract the areas.

Area of the shaded figureArea of square Area of semicircle

100 cm^2 25.12 cm^2

74.88 cm^2

So the area of the shaded figure is about 74.88 square centimeters.

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The diameter of the

semicircle is 8 cm,

so its radius is 4 cm.