   Chapter 8.CT, Problem 13CT Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

In the figure, a square is inscribed in a circle. If each side of the square measures 4 2 in., find an expression for the exact area of the shaded region. To determine

To find:

An expression for the exact area of the shaded region.

Explanation

Given:

In the fig, a square is inscribed in a circle. If each side of the square measures 42 in.

Theorem:

1. The area A of a circle whose radius has the length r is given by the formula, A=πr2.

2. The area A of the square whose length of the side a is given by A=a2.

From the given, the lengths of the side of the square is 42 in.

Here a=42 and d=a2+a2=2a2=a2, then r=d2=a22=a2

The area of the shaded region = Area of the circle – Area of the square

A=πr2-a2

A=πa22-a2

A=πa22-a2

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