Question

Find the area of the shaded portion in the square. Show all work for full credit.

Answer 1

Answer:

36 - 9 pi

Step-by-step explanation:

First of all, you need to find the area of the whole square. The formula for areas of squares is A = s^2. Since the side = 6 ---->  

A = 6^2 ----> A = 36. So the area of the whole square is 36.  

Next, imagine that the big sector is part of a circle. With this information, you can figure out the area of the 'circle' by doing A = pi * r^2 ---> since one of the sides of the square with a measure of 6 is also the radius of the 'circle', the radius is equal to 6 ----> A = pi * 6^2 ----> A = 36 pi. So the area of the circle is 36 pi.  

Now you need to find the area of the sector. Since the measure of the sector's arc is 90 degrees (because the angle is 90 degrees), you would do 90/360 = 1/4. Then do 1/4 times the area of the circle, and you get 9 pi.

Finally, to get the area of the shaded part, you would need to do the area of the square minus the area of the sector:

36 - 9 pi. This is the exact answer. The approximate answer would be 7.73.

Hope this helps! :)

Answer 2

Area of square = 6 x 6 = 36
Area of circle = pi r^2 = 3.14 x 6^3 = 3.14 x 36 = 113.04
1/4 of circle = 113.04 / 4 = 28.26

Area of shaded = 36 - 28.26 = 7.74

answer
7.74