Math Problem : J.3 Overlapped sector and trapezoid

The figure below is a graphic which overlapped sector with 10 cm in radius, 90 degrees of central angles and trapezoid. 

Find the length of X on condition that the area of A and B is equal.

Pi is assumed to be 3.

Answer

4 cm

Solution

What the area of A and B is equal means that the area of sector and trapezoid is equal. 

The area of sector is 10 × 10 × 3 /4 = 75 cm². 

The trapezoidal area is (11 + X) × 10/2=75 cm². 

Therefore, X = 75 ×  2 / 10 - 11 = 4 cm.