In the square below, the four quarter-circles are congruent. Find the shaded region. If necessary, round your answer two decimal places.

Question

anonymous · Answer

attachment

unklerhaukus · Answer

The shaded region is the area of a square minus the area of a circle

unklerhaukus · Answer

the square has sides lengths of 4+4=8 units
 
the circle has radius 4 units

anonymous · Answer

Is the 4 only half of 1 side, or a whole side?

anonymous · Answer

half of one side, which would make it the circles diameter right?

anonymous · Answer

The radius actually

anonymous · Answer

So the area of the circle is 50.24?

anonymous · Answer

So each side is 8. This means that the area is 8*8 = 64

The area of a circle is given by 
$$pir ^{2}$$


Since r =4

Area = 64- 16pi

anonymous · Answer

Is the area 9.76?

anonymous · Answer

yes the area of the circle is 50.27. Now the area of the WHOLE square is 8*8

just subtract 50.27 from 64

anonymous · Answer

Should be 13.73

anonymous · Answer

How did you get 9.76?

anonymous · Answer

Woops just did the math wrong, but thank you very much!

anonymous · Answer

No problem!