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The area of the shaded region enclosed in a semicircle of diameter
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Answer to Problem 13CT
Solution:
The area of the shaded region is
Explanation of Solution
Given information:
A shaded region is as shown in the figure below:
A semicircle of diameter
The length of the chord
To find the area of the shaded region, subtract the area of the triangle
Area of semicircle is
Here, diameter of the semicircle is
By substituting value of
Now,
Thus, by using Pythagorean Theorem
Thus, length of
Area of triangle
Therefore, area of the shaded region
Thus, the area of the shaded region is
Chapter 8 Solutions
Precalculus Enhanced with Graphing Utilities
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