Question

PLEASE HELP IM DOING SO BAD ALREADY I NEED A GOOD GRADE. In the square below, the four quarter-circles are congruent. Find the area of the shaded region. If necessary round your answer to two decimal places. WRONG ANSWERS WILL BE REPORTED

Answer 1

I'm assuming a quarter-circle is exactly 1/4 of a circle.  Thus if you have 4 congruent quarter-circles, that should mean they make a complete circle.

If that is the case, then we can find the area of the full circle using pi*r^2.

So the area of the circle is 5^2*pi or 25pi.

To find the area of the shaded region, we subtract the area of the circle from the area of the square.

The area of the square is 10^2 or 100.

So the area of the shaded region is 100 - 25pi.

My calculator says that equals roughly 21.46