11-7 Area of Complex Figures11-7 Area of Complex Figures(pages 498-500)(pages 498-500)

Standard P8

A complex figurecomplex figure is made of circles, rectangles, squares, and other two-dimensional figures.

To find the area of a complex figure, “cut” the figure into familiar figures whose areas you already know how to find.

Remember your formulas…

Example #1: Find the area of the complex figure.

Area of triangleA = ½bhA = ½· 10 • 6A = ½ • 60A = 30 ft2

The figure can be separated into a square and a triangle.

Area of squareA = s2

A = 102

A = 100 ft2

Add the areas of the simple figures, 100 + 30. The area of the complex figure is 130 square feet or 130 ft2.

Example 2: Find the area of the complex figure

• The figure can be separated into a semicircle and a triangle.

Area of semicircle 2

2

1rA

222

1 A

23.6 inA

Example 2 (continued)

Area of triangle

bhA2

1

5.342

1A

7A

Add the areas together: 6.3 + 7 = 13.3

The area of the figure is about 13.3 in2.

Example #3

The plans for the tabletop of a desk are shown.

In your answer document, determine how many square feet of wood will be needed to build the tabletop if one square represents half-square foot. Provide proof of your findings by showing your work and explain your answer.

Break the desk into familiar figures.

Find the area of the “pieces” of the desk in square units and combine them (add them together.)

Multiply this result by 0.5 to find the area of the desk in square feet.

What do you need to do first?

SHORT ANSWER (2 Points):“Triangle a” A= ½•bh

Rectangle A=bh

“Triangle c” A= ½*bh

“Triangle a” A= 4.5

Rectangle B A=24

“Triangle c” A= 9

4.5 + 24 + 9 = 37.5 u2

37.5 u2 • 0.5 = 18.75 ft2

So, 18.75 square feet of wood is needed to build the desk.

Find the Area of the Complex Figures