SOLUTION: In the diagram below, ABCD is a parallelogram with AB=42 cm. Arc AD is a semi-circle. The area of the parallelogram is 504cm2, and angle ADC = 60 degrees. Find the area of the shad

Question 1149185: In the diagram below, ABCD is a parallelogram with AB=42 cm. Arc AD is a semi-circle. The area of the parallelogram is 504cm2, and angle ADC = 60 degrees. Find the area of the shaded region in cm2.
Diagram: https://imgur.com/a/JyfuGQN
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let x be the length of AD, the base of the parallelogram.

The height of the parallelogram is

The area, 504, is base times height:

AD is the diameter of the semicircle, length x=8*sqrt(3); the radius of the semicircle is 4*sqrt(3). The area of the semicircle is

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