Rhombus diagonals are perpendicular bisectors

All sides equal; diagonals bisect each other at right angles and bisect the vertex angles.

Key formulas

A rhombus is a parallelogram with equal sides. Diagonals are perpendicular and bisect each other.

Area = half product of diagonals. Diagonals 6 and 8 → area 24.

Half-diagonals 3 and 4 → side 5 by Pythagoras.

Problem. A rhombus has diagonals 6 cm and 8 cm. Find its side length and area.

Solution. Half-diagonals 3 and 4 form a right triangle: side = 5 cm. Area = (d₁d₂)/2 = 24 cm².

A square is a rhombus with equal diagonals.

Diagonals 10 and 24. Rhombus side is:

Only if the rhombus is a square.