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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? 

 

 Aug 9, 2020
 #1
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It's a:33,563squre units. 

 Aug 9, 2020
 #3
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Jon Jon, you fat-fingered the last digit ... should be 562 not 563. 

Guest Aug 9, 2020
 #4
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oh.... sorry about that....

JonathanF.Shin  Aug 10, 2020
 #2
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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)(502) 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.

 

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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 Aug 9, 2020

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