Formula

Area from perpendicular diagonals

Mensuration • Plane Figures • Quadrilateral

Formula

A = \frac{1}{2} d_{1} d_{2}

If the diagonals of a quadrilateral are perpendicular and have lengths

d_{1}

and

d_{2}

, its area is

\frac{1}{2} d_{1} d_{2}

. This covers every rhombus and every kite, and in particular the square, where

d_{1} = d_{2}

How to use it

1Reach for it the moment a quadrilateral is described as a rhombus, a kite, or as having all four sides equal — the perpendicularity is then automatic and need not be given.
2Only the two diagonals are needed, so there is no reason to find the side or a height.
3Run it backwards to recover a diagonal: $d_{2} = \frac{2 A}{d _{1}}$ .
4If the diagonals are given as a ratio and a sum, split the sum into the parts of the ratio FIRST — a $1 : 2$ ratio has three parts, not two.

A kite has diagonals of lengths

10

cm and

7

cm. Find its area.

Step-by-step

1
$A = \frac{1}{2} \times 10 \times 7$
Why: The diagonals of a kite are perpendicular, so the half-product applies.
2
$= 35$ cm $^{2}$

Answer

35

^{2}

Watch out

The diagonals must be PERPENDICULAR. A general parallelogram's diagonals bisect each other without being perpendicular, and for it

\frac{1}{2} d_{1} d_{2}

overstates the area — use base times height instead.

Builds on

Also known as

area of a rhombus, area of a kite, half the product of the diagonals, rhombus area from diagonals, quadrilateral with perpendicular diagonals