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Area of a Kite

A kite has two pairs of adjacent sides that are equal, or joining two isosceles triangles with the same base will form a kite.

So the area of a kite can be found by dividing the figure into two equal triangles along one of the diagonals.

area of a kite_1

Area of kite  =  area of triangle 1 + area of triangle 2

=  1/2y(x – a)  +  1/2ya

=  1/2xy  –  1/2ya  +  1/2ya

=  1/2xy

Using the above, we can write the area of a kite to be equal to half the product of its two diagonals.

 

area of a kite_2Example 1 : What is the area of this kite?

 

Splitting the kite along the long diagonal gives us two triangles.

area of a kite_3

Area of kite  =  Area of triangle 1 + Area of triangle 2

=  1/2x 25 x 7  +  1/2x 25 x 7

=  87.5 + 87.5

=  175 cm2

 

Using the formula, we can also obtain the area of this kite.

A = 1/2xy

1/2x 25 x 14

= 175 cm2

 

area of a kite_4Example 2 : Calculate the area of this kite.

Splitting along the longer diagonal, we get two triangles.

Area of kite  =  area of triangle 1 + area of triangle 2

=  1/2x 16 x 5  +  1/2x 16 x 5

=  40 + 40

=  80 cm2

We can also obtain the area of this kite using the formula.

A  =  1/2xy

=  1/2x 16 x 10

=  80 cm2