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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
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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

 

 

cool cool cool

CPhill  Aug 26, 2017
edited by CPhill  Aug 26, 2017

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