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Two Questions about Trapezoids

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Hi, I needed some help with these two trapezoid questions I couldn't understand. 

1) ABCD is a trapezoid with bases AB and DC. We know that Angle C=60 Degrees and Angle D=45 Degrees. If AB=5-2sqrt3 and BC=4, what is $DC?

2) The ratio of the four sides of a trapezoid is 2:1:1:1. The area of the trapezoid is 27sqrt 3. Find the length of the median of the trapezoid.

 Dec 15, 2019

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1) Extend AD and BC to meet at P.  Then you get a 30-60-90 triangle and a 45-45-90 triangles, so by Pythagoras, CD = (6 - 2*sqrt(3)) + (4 + 2*sqrt(3)) = 10.

 

2) Using the area condition, the bases of the trapezoid work out to 8 and 16, so the median is (8 + 16)/2 = 12.

 Dec 16, 2019

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