An isosceles trapezoid is inscribed in a semicircle as shown below, such that the three shaded regions are congruent. The radius of the semicircle is one meter. How many meters are in the perimeter of the trapezoid? Express your answer as a decimal to the nearest tenth.
+130477 If the shaded regions are equal.....then the chords that comprise the top and sides of the trapezoid must be equal
Call the top two vertices A and B and the center 0
Then . connecting the top two vertices to the center will form triangle AOB with angle AOB = 60° and OA, OB = 1 m
Using the Law of Cosines we can find chord AB as :
AB^2 = OA^2 + OB^2 - 2(OA * OB) cos (AOB)
AB^2 = 1^2 + 1^2 - 2 ( 1 * 1) (1/2)
AB^2 = 2 - 1
AB^2 = 1
AB = 1
The perimeter of the trapezoid = 3AB + diameter = 3 (1) + 2 = 5 m
