Question

How is the formula for the area of a rhombus is derived?

Answer 1

To reiterate:

In a rhombus, the diagonals are perpendicular bisectors.

If the diagonals are `p` and `q`, the new bisected portions are `p/2` and `q/2`, leaving `4` congruent right triangles with bases and heights of `p/2` and `q/2`.

To find the area of one of the triangles, use the formula `A=1/2bh`.

`A=1/2(p/2)(q/2)=(pq)/8`

Since there are `4` of the triangles, the area of the total rhombus is `4((pq)/8)=(pq)/2`.