Question

In the figure below, a circle of radius 4 inches is inscribed in a trapezoid ABCD whose longer base is 12 inches. Find the area of the trapezoid. Give exact answer including units.

Answer 1

area of a trapezoid = (a+b)/2 * h

b = 12 ; h = (4x2)= 8 ; a = ?

I'm assuming that a = 6. Based on the figure, the upper base is shorter compared to the diameter of the inscribed circle. It seems as though it only covers 75% of the diameter. So, 8 is the diameter. 75% of it is 6.

Area = (6inches +12 inches )/2 * 8 inches
A = 18 inches/2 * 8 inches
A = 9 inches * 8 inches
A = 72 square inches.

The area of the trapezoid is 72 square inches.