Basic College Mathematics (10th Edition)

Published by Pearson
ISBN 10:
ISBN 13:

Chapter 8 - Geometry - Review Exercises - Page 614: 44

Answer

$498.9~ft^2$

Work Step by Step

We can find the green area in two steps: - Find area of whole rectangle (21 ft x 32 ft) - Find area of white semi-circle (diameter 21 ft) Subtracting the two areas gives the green area. Area of rectangle: We know that the area of a rectangle is given by: $Area=length*width$ $A=lw$ So we have: $A=21*32=672~ft^2$ Area of semi-circle: We know that the area of a circle is given by: $A=\pi*radius^2$ $A=\pi r^2$ For a semi circle, the area is half of a circle: $A=\frac{1}{2}\pi r^2$ So we have ($radius=diameter/2=21/2$): $A=\frac{1}{2}\pi (21/2)^2$ $A=173.1~ft^2$ We subtract the two areas: $672-173.1=498.9~ft^2$
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