Diagonals at right angle

In the trapezoid ABCD, this is given:
AB=12cm
CD=4cm
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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