Above the Two Circles

Geometry Level 2

The two circles have the same size and area. What is the area of the red-shaded part written in the nearest ten-thousandths?


The answer is 1.3144.

Kaizen Cyrus by Kaizen Cyrus , 18, Philippines

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2 solutions

Note: The diagram is not drawn to scale Note: The diagram is not drawn to scale Consider my diagram. Observed that the area of the yellow region is the area of a semi-circle. The area of the red region is equal to the area of the rectangle with dimensions 1.75 x 3.5 \text{1.75 x 3.5} minus the area of the yellow region. We have

area of red region = 1.75 ( 3.5 ) − 1 2 π ( 1.75 ) 2 ≈ 1.3144 \text{area of red region} = 1.75(3.5)-\dfrac{1}{2} \pi (1.75)^2 \approx \large{\boxed{1.3144}}

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Jul 22, 2018

1.7 5 2 ( 2 − π 2 ) ≈ 1.3144 1.75^2(2-\dfrac\pi2)\approx1.3144

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