   Chapter 8.4, Problem 46E 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

A tabletop is semicircular when its three congruent drop-leaves are used. By how much has the tables area increased when the drop leaves (shaded area) 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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