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
Algebra.Com
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): You can put this solution on YOUR website!
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
RELATED QUESTIONS
A semicircle is inscribed in a rectangle with area 144 square centimeters. In square cm,
(answered by lwsshak3)
Find the rectangle of largest area that can be inscribed in a semicircle of radius R,... (answered by jorel1380)
What is the largest size of a rectangle that can be inscribed in a semicircle of radius 1 (answered by ikleyn)
The sides of triangle XYZ are XY = XZ = 25 and YZ = 40. A semicircle is inscribed in... (answered by ikleyn,greenestamps)
An isosceles right triangle ACB is inscribed in a semicircle with a diameter of length... (answered by Alan3354)
what is the area of a semicircle with diameter 20... (answered by richwmiller)
A rectangle is inscribed in a semicircle of radius
r = 12. Find a function that models... (answered by fractalier)
a semicircle of radius r =2x is inscribed in a rectangle so that the diameter of the... (answered by KMST)
a piece of wire that has been bent in the form of a semicircle including the bounding... (answered by mananth)