SOLUTION: In the diagram, ABCD is a parallelogram with AB=37 cm. AD is a semi- circle. The area of the parallelogram is 518 cm^2, and < ADC = 60°. Find the area of the shaded region in cm

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Question 1209055: In the diagram, ABCD is a parallelogram with AB=37 cm. AD is a semi- circle.
The area of the parallelogram is 518 cm^2, and < ADC = 60°. Find the area of the shaded region in cm^2.
https://ibb.co/xs0HGmk
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.
In the diagram, ABCD is a parallelogram with AB=37 cm. AD is a semi- circle.
The area of the parallelogram is 518 cm^2, and < ADC = 60°.
Find the area of the shaded region in cm^2.
https://ibb.co/xs0HGmk
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Use the formula for the area of a parallelogram

    area = ,


where "a" and "b" are any two adjacent sides of the parallelogram and    is
the concluded angle between these sides.


In our case AB = 37, AD is unknown,  = 180°-60° = 120°. So, we have this equation

    518 = 37*AD*sin(120°) = 37**AD,

hence

    AD =  =  cm.


AD is the diameter, the shaded area is the semi-circle.


Hence, the area of the shaded area is  

     =  =  =  =  =  = 102.625 cm^2  (approximately).


ANSWER.  The area of the shaded area is    cm^2,  or  about  102.625 cm^2.

Solved.



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