   Chapter 8.4, Problem 46E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# A tabletop is semicircular when its three congruent drop-leaves are used. By how much has the tables area increased when the drop leaves increased. Give the answer to the nearest whole percent. To determine

To Find:

The percentage of increased area of the tabletop.

Explanation

The tabletop contains three congruent triangles.

The side of the triangle is equal to the radius of the circle.

Therefore, s=r.

The area of the equilateral triangle is A=3s24=3r24.

Therefore, the area of the three triangles is A=33r24.

The area of the semicircle is A=12πr2.

To find the area of the drop-leaves of the tabletop, subtract the area of three triangles from the area of the semicircle

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