ABCD is a square with AB = 18 cm. Arcs BC and CD are semicircles. Express the area of the shaded region, in square centimeters, and in terms of pi.
This seems trickier than it really is
Look at the following figure :
Note that since the sides of the square = 18....then DB = sqrt 2*18 = AC
E is the center of the square so BE = CE = sqrt (2)*10
And angle CEB = 90°
And the circle has a radius of 18
So....if we take the area of 1/2 of this circle and subtract the area of triangle CEB we will have the same area as the shaded region
Area of half-circle with radius of 12 = pi (6/2)^2 / 2 = 18*pi
Area of triangle CEB = area of an isosceles triangle with equal sides of sqrt (2)/2 and an included angle of 90° =
(1/2) [ sqrt (2) / 2 ] ^2 *sin 90° = 12
So....the shaded area = 16*pi - 4
