Area of a Rhombus

A rhombus is a quadrilateral with four equal sides. If you know the lengths of its two diagonals, the area follows immediately: multiply them and halve the result.

• $S$ — the area
• $d_1$ — the first diagonal
• $d_2$ — the second diagonal

Example

With the defaults, $d_1 = 6$ and $d_2 = 8$:

The area is 24.

Where the formula comes from

The diagonals of a rhombus cross at right angles and bisect each other. Draw a rectangle around the rhombus with sides $d_1$ and $d_2$, aligned with those diagonals: the rhombus sits inside and covers exactly half of it. Hence $\dfrac{d_1 d_2}{2}$.

Watch out

This formula belongs to quadrilaterals whose diagonals meet at right angles, which means rhombuses, squares and kites. It fails for a rectangle or a general parallelogram, where the diagonals are not perpendicular. If instead you know a side $a$ and an interior angle $\theta$, the area is $S = a^2 \sin\theta$. And because a rhombus is also a parallelogram, $S = b h$ works whenever you know a base and its height.