SOLUTION: How do you find the area of a trapezoid when you are only given the bases, 8 and 16 and one of the angles is 60. How do I figure out the height with the 30,60,90?

Question 573525: How do you find the area of a trapezoid when you are only given the bases, 8 and 16 and one of the angles is 60. How do I figure out the height with the 30,60,90?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do you find the area of a trapezoid when you are only given the bases, 8 and 16 and one of the angles is 60. How do I figure out the height with the 30,60,90?
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Draw the picture with the top base being 8.
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Draw a line segment from the upper left vertex to the base.
Draw a line segment from the upper right vertex to the base.
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See the rectangle you have formed; the top and bottom are 8.
That leaves 4 of the base on the left and 4 of the base on the right.
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You have a 30-60 degree triangle with side opposite the 30 degree
angle = 4; so the slant height = 8
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Solve for the vertical height (H)
(H)^2 + 4^2 = 8^2
H^2 = 64-16 = 48
H = 4sqrt(3)
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Area of trapezoid = (1/2)h(sum of bases)
= (1/2)(4sqrt(3))(24)
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= 48sqrt(3) sq units
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Cheers,
Stan H.
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