Question

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

Answer 1

Well, what I would do [not sure if it's the correct way], is use the white area as a sector of a circle. The top right of the box is the center of the circle, so the radius is 6.
Then, by the white portion being one quarter of the circle (90° out of 360°), I could calculate the that pink shaded region = the total square (6×6) minus the white sector.
So area (A) of white sector (s): A(s) = 1/4×pi×r^2
$A(s) = \frac{\pi {r}^{2} }{4} = \frac{\pi \times {6}^{2} }{4} \\ A(s) = \frac{36\pi}{4} = \frac{9\pi}{1} = 9x3.142 \\ A(s) = 28.27$
36 - 28.27 = 7.73

Answer 2

Answer:

$9\pi -36$

Step-by-step explanation:

In order to find the area of the shaded area you first need to find the area of the circle segment. The easiest way to do this would be to use the equation: $A=\pi r^2$ you would substitute r with the radius which in this case is 6: $A=\pi 6^2$

This would give you the answer $36\pi$

Because the picture only shows you 1/4 of the circle, you will need to divide $36\pi$ by 4. This gives you $9\pi$.

Now, in order to find the area of the shaded area you will need to subtract $9\pi$ by the area of the square. The square has side lengths of 6, and in order to find the area, you will multiply 6 by 6 to get 36.

Now you will subtract to get: $9\pi -36$