0
$\begingroup$

By definition parallelograms are special type of trapezoids. Given a trapezoid with known sides one can calculate its area according to wikipedia. But in order to calculate the area of a parallelogram you need to know its height. I find this paradoxical. Can someone help clarifying this?

Edit: What I think I want to know is why trapezoid in general are solid(if that's the right word) but parallelograms are not. Rhombi are parallelograms. I can imagine changing a rhombus's diagonals (hence its area) without changing its sides.

$\endgroup$
0
$\begingroup$

There is no paradox. The area of a trapezoid can be given by $$A = (b_1 + b_2)h/2,$$ where $b_1$ and $b_2$ are the lengths of the two parallel sides, and $h$ is the distance (height) between the parallel sides.

In a parallelogram, we have the special case $b_1 = b_2 = b$, thus the formula reduces to $$A = (2b)h/2 = bh.$$

$\endgroup$
  • $\begingroup$ what I meant was you have to know the height of a parallelogram to find its area you cannot calculate the area of a parallelogram just by its sides. $\endgroup$ – nww12 Oct 5 '15 at 20:26
  • $\begingroup$ This is because, given the side lengths of a trapezoid and knowledge of which two sides are parallel, a general (nondegenerate) trapezoid has more information about its shape than a parallelogram. A trapezoid will have in general four unique side lengths. A parallelogram has only two. $\endgroup$ – heropup Oct 5 '15 at 20:32
0
$\begingroup$

Note that the Wikipedia formula involves the denominator $|b-a|$ which becomes $0$ in the case of the parallelogram; i.e. the formula only applies for non-parallelogram trapezoids.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.