+1348 In the figure, triangle $ABC$ is inscribed in a semicircle with diameter $AC$ of length $20$ inches, and $AB = 10$ inches. When the area of the shaded region, in square inches, is expressed in the form $a\pi - b,$ what is the value of $a + b\,?$
+129771 Area of semi-circle = (1/2) pi (diameter / 2)^2 = (1/2) pi (10)^2 = 50pi (1)
BC = sqrt [ 20^2 -10^2 ] = sqrt [ 300 ] = 10sqrt 3
Area of right triangle ABC = (1/2) AB * BC = (1/2) (10) (10sqrt 3) = 50 sqrt 3 (2)
Shaded area = (1) - (2) = 50 pi - 50sqrt 3
a + b = 50 + 50sqrt 3 ≈ 136.6
