The area of the shaded region.
Answer to Problem 32PPS
The area of the shaded region is 69.7 sq. ft. (approx.).
Explanation of Solution
Given: A
Concept Used: The formula for the area of circle with radius r is given by-
Area of circle
The formula for the area of a square with side a is given by-
Area of square
The area of any shaded region can be found by subtracting the unshaded region from the total region.
Calculations: The total region in this case is a square with side 18 ft. Thus, area of total region-
Total area = Area of the square
The unshaded region is a square whose diameter is equal to that of the side of the square as every side is a tangent to the circle. Hence, diameter of the circle is also 18 ft. Hence, the radius of the circle is given by-
Radius
Therefore, area of the unshaded region is given by-
Unshaded area = Area of circle
Therefore, total area of the shaded region is-
Shaded area = Area of square
Thus, area of the shaded region is 69.7 sq. ft (approx.).
Chapter 11 Solutions
Geometry, Student Edition
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