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 square meters are in the area of the trapezoid? Express your answer as a decimal to the nearest tenth.

AdminMod2
Aug 26, 2017

#1**+2 **

If the shaded regions have equal areas....then the chords forming part of their boundaries have equal length.....then each chord must span 60° and radii drawn from the center of the semi-circle to each of the upper vertices of the trapezoid will form three congruent equilateral triangles whose sides will all equal 1 meter

Then the area of the trapezoid is :

3 (1/2) sin 60 = 3 (1/2) (√3) /2 = (3/4)√3 m^2 ≈ 1.3 m^2

CPhill
Aug 26, 2017