Diagonals at right angle

In the trapezoid ABCD, this is given:
And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?

Correct answer:

S =  64 cm2

Step-by-step explanation:

a=12 cm c=4 cm  a:c = h1:h2  h = h1+h2  h1=a/2=12/2=6 cm h2=c/2=4/2=2 cm  h=h1+h2=6+2=8 cm  S=2a+c h=212+4 8=64 cm2

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Showing 1 comment:
Math student
I don't think the solution is correct.  The height is the radius if and only if the trapezoid is symmetrical.  But it doesn't have to be.  In fact, take a line segment of length 12 and start a 20 degree angle from one side and 70 from the other (for the diagonals). Intersect them and keep going until there is 4 long parallel line. Then increase the 20 degree angle - the height will increase and the area too.

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