   Chapter 8.CR, Problem 17CR 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

If A C ¯ is a diameter of O, find the area of the shaded triangle. Exercise 17

To determine

To find:

The area of the shaded triangle.

Explanation

Theorem:

1. The area A of a triangle whose base has length b and whose corresponding altitude has length h is given by

A=12bh

2. The area A of a square whose sides are each of length s is given by A=s2

Calculation:

Sketch the following diagram:

To find ΔAABC:

ΔAABC=12bh=12×11×12=11×6=66 cm2

To find ABFDE:

ABFDE=s2=42=16cm2

To find ΔACDF:

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