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Both diagrams show squares of congruent lengths. On the left, the rhombus is formed by two midpoints on the square and two intersection points of identical circles. The yellow area is shaded as shown above.

Which diagram has the greatest amount of shaded area?

 

 Feb 1, 2021

Best Answer 

 #2
avatar+536 
+1

Say the square side length is 16. The right picture would have an area of 16pi.

The area of the whole rhombus would be 64.

IF we made a square right around the star, we get a square with 4 quarter circles on each corner.

The square area would be 64 and the 4 quarter circles are just on the whole circle with a radius of 4, with an area of 16pi.

So the area of the cross would be 64-16pi.

Subtracting that from the original rhombus we get 64-(64-16pi) or 16pi.

They are the same.

 Feb 1, 2021
 #1
avatar+18 
+1

I'm not sure if I'm right but I think it is the one on the left (unless having the same area is an option).

 Feb 1, 2021
 #2
avatar+536 
+1
Best Answer

Say the square side length is 16. The right picture would have an area of 16pi.

The area of the whole rhombus would be 64.

IF we made a square right around the star, we get a square with 4 quarter circles on each corner.

The square area would be 64 and the 4 quarter circles are just on the whole circle with a radius of 4, with an area of 16pi.

So the area of the cross would be 64-16pi.

Subtracting that from the original rhombus we get 64-(64-16pi) or 16pi.

They are the same.

MooMooooMooM Feb 1, 2021
 #3
avatar+116126 
0

Excellent, 4M   !!!!!

 

 

 

cool cool cool

CPhill  Feb 1, 2021

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