   Chapter 8.2, Problem 54E 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

Trapezoid ABCD (not shown) is inscribed in ⊙ O so that side D C - is a diameter of ⊙ O . If D C   =   10 and A B   =   6 , find the exact area of trapezoid ABCD.

To determine

To Find:

The exact area of trapezoid ABCD if it is inscribed in circle O.

Explanation

Formula Used:

1. Pythagorean theorem for the right angle triangle ABC for the hypotenuse AC,

AC2=AB2+BC2.

2. The area A of a trapezoid whose bases have lengths b1 and b2 and whose altitude has length h is given by A=12h(b1+b2)

It is given that the trapezoid ABCD is inscribed in O with side DC- is a diameter of O.

Also given that DC = 10 and AB = 6.

Let’s draw inscribed trapezoid ABCD with diameter of the circle O as 10.

Since the bases of the trapezoid are always parallel and it is inscribed in the circle O with diameter CD=10, it must be an isosceles trapezoid. That is, the non-parallel sides must be in equal measure.

Let’s draw altitudes AE and BF of the trapezoid from the points A and B to the line CD

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