a diagonal of an isosceles trapezoid measures 20 units and makes an angle of 30 degrees with the base. If one of the congruent sides measures 15 units, find the area of the trapezoid.

Question

anonymous · Answer

based on my computation the area is 454.81 square units. But I'm not sure if that's the correct answer.
please help!

ranga · Answer

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ranga · Answer

BE = 20cos(30)
DE = 20sin(30) = height of trapezoid

AE = sqrt(15^2 - DE^2)

So the same on the right side and you can find the length of AB and CD.

Area = 1/2(AB + CD)DE

anonymous · Answer

It's the same of how I illustrate the figure! :)

anonymous · Answer

198.41 ??
am I correct?

ranga · Answer

BE = 17.32, DE = 10, AE = 11.18
BA = BE + EA = 28.5
CD = AB - 2(AE) = 28.5 - 2(11.18) = 6.14

Area = 0.5(AB + CD)(DE) = .5(28.5 + 6.14)(11.18) = 193.64

I am getting 193.64 but haven't double checked my calculations.

anonymous · Answer

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is this possible?