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Let A, B, C, be three points on a line such that AB = 2 and BC = 4. Semicircles are drawn with diameters AB, AC, and BC. Find the area of the shaded region.

 

Guest Feb 27, 2017
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The area of the shaded region wiil be the area of the semi-circle with the diameter AC mnus the areas of the two smaller semi-circles with diameters  AB and AC

 

Radius of  large semi-circle with diameter AC  = [AB + BC] / 2  =  [ 2 + 4 ] / 2 = 6/2  = 3

 

And the radiuses of AB and BC  = 1  and 2 , respectively

 

So  the shaded area  =

 

(1/2) pi [ 3^2 - 1^2 - 2^2]  = (1/2)  pi [ 9 - 1 - 4 ]   = (1/2) 4pi units^2  = 2 pi units^2

≈  6.28 units^2

 

 

cool cool cool

CPhill  Feb 27, 2017

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