Question

Find the area of the kite

Answer 1

Given:

A figure of a kite.

To find:

The area of the given kite.

Solution:

The area of a kite is the half of the product of its diagonals.

$A=\dfrac{d_1d_2}{2}$             ...(i)

Where, $d_1,d_2$ are two diagonals of the kite.

From the given figure it is clear that the length of one diagonal is the sum of 12 and 8.

$d_1=12+8$

$d_1=20$

Let the second diagonal be 2x. The first diagonals bisect the second diagonal. So, the length of one parts of the diagonal is x.

Diagonals of a kite are perpendicular to each other. Using Pythagoras theorem, we get

$Hypotenuse^2=Perpendicular^2+Base^2$

$13^2=x^2+12^2$

$169-144=x^2$

$25=x^2$

$5=x$

The length of second diagonal is:

$d_2=2x$

$d_2=2(5)$

$d_2=10$

Substituting $d_1=20,d_2=10$ in (i), we get

$A=\dfrac{20\times 10}{2}$

$A=\dfrac{200}{2}$

$A=100$

Therefore, the area of the kite is 100 square units.