In the diagram, the vertices of the square lie at the centers of the four partial circles. What is the area of the entire shape?

Guest Aug 9, 2020

#2**+1 **

One side of the square is 100 so the area of the square is 10,000.

The radius of a circle is 50 so the area of the whole circle would be (3**.**1416)(50^{2}) is 7,854

but you don't count the whole circle because part of the square overlaps a fourth of it

So the area of the remaining three-fourths of the circle is 5,890**.**5

There are four of these "partial" circles so their total area is (4)(5,890**.**5) is 23,562

Add the area of the square plus the four partial circles 10,000 + 23,562 = **33,562**

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Guest Aug 9, 2020