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Square ABCD is inscribed in a circle with diameter BD of length 2 units. Segment AB is the
diameter of the half-circle on top of the square. What is the area of the shaded region, in square units?
Express your answer as a common fraction. Please show your work.

 

 Oct 23, 2022
 #1
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The shaded area is (pi - 1)/2.

 Oct 23, 2022
 #2
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(All of these values are found using simple area formulas, or length formulas derived from the Pythagorean Theorem)

 

AB is the square root of 2.

 

The area of the semicircle is pi/2.

 

The area of the square is 2.

 

The area of the circle around the square is pi.

 

The area of the part of the circle between arc AB and AB is (pi-2)/4

 

The area of the lune (shaded part) is pi/2 - (pi-2)/4 = pi/4 + 1/2

 

(I think)

 Oct 23, 2022

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