   Chapter 8.5, Problem 3E 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 semicircular region shaded D Q = 6 " .a) Find the exact perimeter of the region.b) Find the exact area of the region. To determine

(a)

To find:

The exact perimeter of the shaded region.

Explanation

Definition:

Semicircle is one half of the circle.

Since the semicircular region corresponds to a central angle of 180, the perimeter of semicircle is one half of the circumference of the circle.

Formula:

If r is the radius of circle,

Psemicircle=12× Circumference of circle =12×2πr=πr.

Thus, Psemicircle=πr.

Calculation:

Given that DQ=6. Thus, radius of circle measures 6.

Let’s substitute the value of r as 6 in the formula

To determine

(b)

To find:

The exact area of the shaded region.

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