   Chapter 8.CT, Problem 15CT 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

Find the exact area of the shaded segment. To determine

To find:

The exact area of the shaded segment.

Explanation

Given:

The figure below.

Theorem:

1. In a circle of radius length r, the area A of a sector whose arc has degree measure m is given by A=m360πr2.

2. The area A of an isosceles triangle whose length of the equal sides r is given by A=12r2.

From the figure given, r=12 in., and m=90.

Area of the segment = Area of the sector – Area of the triangle

A=m360πr2-12

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