Chapter 8.4, Problem 24E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# In exercises 23-26, find the exact areas of shaded region.

To determine

To Find:

The areas of the shaded region.

Explanation

To find the area of the shaded region of the circle, find the area of the circle and rectangle and then subtract the area of the rectangle from the area of the circle.

It is given that one side of the square is 8 in and the other side is 6 in.

Therefore, the area of the rectangle is A=bh.

Therefore, A=8â‹…6=48.

The area of the rectangle is 48 in2.

Next, to find the area of the circle, we need radius of the circle.

The radius can be obtained from the diagonal of the rectangle.

The diagonal of the rectangle can be obtained using pythagorus theorem.

According to pythagorus theorem, c2=a2+b2.

Consider a=8â€Šâ€Šâ€Šâ€Šâ€Šandâ€Šâ€Šâ€Šâ€Šâ€Šb=6.

Therefore, c2=82+62=64+36=100

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