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

Algebra ->  Surface-area -> 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      Log On


   

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) About Me  (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

42%2Asin%2860%29+=+42%2A%28sqrt%283%29%2F2%29+=+21%2Asqrt%283%29

The area, 504, is base times height:

504+=+%28x%29%2821%2Asqrt%283%29%29
x+=+504%2F%2821%2Asqrt%283%29%29+=+24%2Fsqrt%283%29+=+8%2Asqrt%283%29

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

%281%2F2%29%28pi%29%284%2Asqrt%283%29%29%5E2+=+24pi