6th Grade Math Textbook, Progress

Use Formulas to Solve Problems

13-19

The stage for the fashion show is shaped like the diagram

shown at the right. The show planners need to order

carpeting to cover the stage floor. What is the area of

the floor that needs to be carpeted?

Notice that the stage is shaped like a triangle attached

to a semicircle.

To find the area of the floor, first find the area of the triangle

and the area of the semicircle. Then find the sum of the areas.

Find the area of the triangle. A
^12 bh

^12 (32 ft 16 ft) 
256 ft^2

Find the area of the semicircle. A
^12 (πr^2 )

A
^12 3.14 (16 ft)^2


401.92 ft^2


402 ft^2

Find the surface area, S, S
256 ft^2 402 ft^2

by adding the two areas. 
658 ft^2

So, the area of the floor that needs to be carpeted

is about 658 square feet.

Round to the nearest whole number.

The area of a semicircle

is half the area of a circle.

Use the figure above for exercise 1.

1. A ribbon banner will be attached around the outside border
   of the stage. How many feet of ribbon are needed? (Round to
   the nearest whole number.)


2. Originally, the show planners were going to
   have a stage shaped like a triangle attached
   to a rectangle. The triangle would have been
   the same size. The rectangle would have
   had the same length as the diameter of the
   semicircle and the same width as the radius
   of the semicircle. What would the area of a
   stage shaped like that be?

32 ft

22.6 ft

16 ft

22.6 ft

16 ft

32 ft

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