Core Connections Integrated II, 2015
CC
Core Connections Integrated II, 2015 View details
4. Section 9.4
Continue to next subchapter

Exercise 137 Page 532

The area of the square minus the area of the circle is twice the region that you are looking for.

About 3.86 m^2

Practice makes perfect

To find the area of the shaded parts below, we can calculate the area of the square and then subtract the area of the circle.

However, we are only interested in the shaded part in the upper right and lower left part of the square.


After we subtract the area of the circle from the square, the four remaining shaded parts are congruent. Therefore, we can find the area of the shaded region by dividing the area of the four shaded parts by 2.
Square-Circle
s^2-π r^2
6^2-π( 3)^2
36-π* 9
36-9π
The area of the four shaded corners of the square is (36-9π) m^2. Finally, we divide this by 2 to obtain the area of two of these areas. 36-9π/2≈ 3.86 m^2