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How would I find the area of a trapezoid if I know the lengths of the "legs" but not the lengths of the parallel sides. So in the attached image, the lengths c and d are known but not the parallel sides, a and b. The angle, beta, is known. The angle between side c and a is 90 degrees as is the angle between c and b.

The only thing I have been able to think of is to draw the line, h, which will allow me to calculate a portion of the length a (h = c and d and beta are known). However, I can't figure out how to get the other portion of the length a, which is also equal to b.

Please excuse the poor quality of the drawing.

enter image description here

rdemyan
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  • please edit your diagram and write your attempts. – Lion Heart Sep 30 '22 at 15:23
  • It's impossible. Sides $a,b$ can be moved like a trombone slide, preserving all the known values. – Parcly Taxel Sep 30 '22 at 15:44
  • Thanks for the comment about the trombone slide. That was very helpful. It made me realize that I needed to take another look at the physical system that I am trying to get the area of (via the trapezoid). After looking at it again, I realize that I can in fact separately calculate the side b. Knowing b, everything else falls in place. I may repost if I need help simplifying the final expression. – rdemyan Sep 30 '22 at 16:12

1 Answers1

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If we know that the angle between side c & b and side c & a is 90 degrees, we can cut through the trapezoid to create a rectangle of side dimension bc. So, the area for this part is bc.

Then, the rest of the shape is a right-angled triangle which its area is (1/2)*(a-b)*c, assuming that side a is parallel to side b.

Therefore, the final area for this trapezoid is bc+(1/2)(a-b)*c

Tatsunori Ono
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