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

#2**0 **

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

CPhill
Feb 27, 2017