SOLUTION: A 1×2 rectangle is inscribed in a semicircle with the longer side on the diameter. What is the area of the semicircle?
(A) π 2 (B) 2π 3 (C
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-> SOLUTION: A 1×2 rectangle is inscribed in a semicircle with the longer side on the diameter. What is the area of the semicircle?
(A) π 2 (B) 2π 3 (C
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Question 1120732: A 1×2 rectangle is inscribed in a semicircle with the longer side on the diameter. What is the area of the semicircle?
(A) π 2 (B) 2π 3 (C) π (D) 4π 3 (E) 5π 3 Answer by solver91311(24713) (Show Source):
Construct a segment from the center of the circle to the point of intersection of the circle and one vertex of the rectangle. You will then form an isosceles right triangle with legs that measure 1 unit. The hypotenuse of this triangle will be a radius of the circle. Calculate the measure of the hypotenuse of the constructed triangle. Then calculate the area of the circle. Then divide the area of the circle by 2 to get the area of the semicircle.
John
My calculator said it, I believe it, that settles it
