Chapter 8.1, Problem 2E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# The area of the square is 12, and the area of the circle is 30. Does the area of the entire shaded region equal 42? Why or why not?

To determine

Whether the area of the entire shaded region is equal to 42?

Explanation

Given,

The area of the square =12Â unit2

The area of the circle =30Â unit2

From the figure,

The area of the circle =12

x+z=12â‹¯(1)

z=12âˆ’x

The area of the square =30

x+y=30â‹¯(2)

y=30âˆ’x

The area of the entire shaded region =42

x+y+z=42â‹¯(3)

If x,y,zâ‰ 0

Substitute y and z value in equation (s)

x+y+<

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