The area of a kite is half the product of the diagonals. A kite is a four-sided figure in which two pairs of adjacent sides are equal. The longest diagonal is the line of symmetry. This line of symmetry bisect two of the angels of the kite. The other two angles are equal. On this page, we will discuss the area of a kite in detail.

## What is the area of a kite?

The area of a kite is the product of the diagonals. i.e 1/2 × the product of the diagonals. The area of a kite is found by multiplying the diagonals of the kite and taking half of it.

## How to find the area of a kite

To find the area of a kite, we take the product (×) of the lengths of the longest and the shortest diagonals of the kite and multiply it by half (1/2). i.e area of a kite = 1/2 × the product of the diagonals. Let’s understand more by working on some examples.

Example 1. The diagonals of a kite are 7cm and 12cm long. Find the area of the kite.

Solution

The area of a kite is

\begin{aligned} &= \frac{1}{2} × \text{the product of the diagonals}\\ &= \frac{1}{2}× 7m × 12m \\ &= \frac{1}{2}×84m^2\\ &= 42m^2\end{aligned}\\ \therefore \text{the area of the kite is }\space 42m^2

This is pretty good, right? let’s look at another example

Example 2: Find the area of the kite below.

Solution

Considering the kite above the lengths of the diagonals are 3cm and 9cm.

Area of a kite is

\begin{aligned}&= \frac{1}{2}× \text{the product of diagonals}\\ &= \frac{1}{2}×3m×9m\\ &= \frac{1}{2}×27m^2\\ &= 13.5m^2\end{aligned}

Example 3. The longest diagonal of a kite is 4 more than the shortest diagonal of the kite. The area of the kite is 5 times the shortest diagonal. If the shortest diagonal is 6m. Find the longer diagonal and the area.

solution

Considering the kite above, the shorter diagonal is = 6m.

The longest diagonal is 4 more than the shortest diagonal i.e (4+6)m = 10m, and the area of the kite is 5 times the shortest diagonal i.e (5×6m)= 30m^{2}

Hence the length of the longest diagonal is = 10m and the area of the kite is = 30m^{2}

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