How to Find the Area of Kite?

Kite

A Kite is a flat shape with straight sides. It has two pairs of equal length with adjacent sides.

Properties of a kite

A kite has two pairs of sides.
Two pairs are equal in length and both sides are adjacent.
Where two pairs of sides meet the angles are equal.
Diagonals cross at right angles.

Area of a Kite

Space enclosed by a kite is called its area. A kite has 4 angles, 4 sides, and 2 diagonals. The area of the square is always expressed in square units like

Area of a kite = $\frac12\;D_1D_2$

How to derive a formula to find the area of a kite

How to Find the Area of Kite — Area of kite

We want to find the area of a kite $ABCD$

The length of the diagonals of ABCD to be $AC=p$ and $BD = q$

Longer diagonal bisects the shorter diagonal at a right angle that is BD bisect AC and $∠AOB=90°$ , $∠BOC=90°$

So,

$AO=OC=AC/2 =p/2$

Area of kite = $Area of triangle ABD + Area of triangle BCD…….(1)$

Area of triangle = $½ (base)(height)$

Area of triangle ABD = $½ (AO)(BD)$

= $½ (p/2) (q)$

= $(pq)/4$

Area of triangle BCD = $½ (OC)(BD)$

= $½ (p/2) (q)$

= $(pq)/4$

By using eq. 1

Area of kite ABCD= $(pq)/4+(pq)/4$

= $(pq)/2$

As we know

$p=AC ,q = BD$

Area of kite = $½ (AC)(BD)$

Leave a Comment Cancel Reply