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# Math ​

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Math

NotSoSmart  Apr 21, 2017
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5.   We first need to find the height of the triangle.....this will also equal the height of the trapezoid on the left

Since the height of the triangle is opposite a 30 degree angle in a 30 - 60 - 90 triangle, its measure is 1/2 of the hypotenuse =  12

And the base is opposite the 60 degree angle....so its length is (√3/2) * hypotenuse  = (√3/2)*24 = 12√3

So.....the area of the triangle  =  1/2 base * height  =  (1/2) (12√3)(12)  = 72√3

The figure on the right  is a trapezoid....its area  =  (1/2) Height ( Top Base + Bottom Base) =

(1/2)(12) (18 + 6)  =  6 * 24   =  144

So.....the correct  answer   is     144 + 72√3

6.  Area  of kite   = (1/2) product of the diagonals  =

(1/2) (5.3 * 6)   =  15.9 ft^2

CPhill  Apr 21, 2017

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