Question

Calculate the area of a rhombus of side 250mm and longer diagonal 400mm​

Answer 1

`60\ 000 mm^2`

Explanation:

Refer to the imagine attached.

First of all, let's remember that in a rhombus diagonals are perpendicular to each other, and cut themselves in half. That allows us to focus on 1/4 of the figure (they gray shaded right triangle in my image.

By aplplying pythagorean theorem (or recognizing a 3-4-5 pythagorean triplet scaled up) you can compute the missing side as
`3 * 50 = 150 mm` long, making the shorter diagonal
`300 mm` long.

At this point you apply the rhombus area formula, with D and d being the two diagonals

`A = \frac12 D* d = \frac12 400 * 300 = 60\ 000 mm^2`

(a bit less than a A4 sheet of paper)