# Kite Shape

By the end of this lesson, you will be able to

- define kite in geometry.
- calculate the area of a kite shape.
- calculate the perimeter of a kite.
- interpret properties of kite shape in geometry.

## Kite

A kite is a simple quadrilateral with two pairs of equal sides where each pair must be adjacent. A kite is a special type of quadrilateral

Each pair of equal adjacent sides shares a common vertex. The diagonals of a kite intersects at right angle to each other

A kite may be convex quadrilateral or concave quadrilateral.

## Area of Kite

Area of a kite can be calculated in several ways.

If the lengths of the two diagonals of a kite are known, the area is half the product of the diagonals.

Suppose, the lengths of the two diagonals are d_{1} are d_{2}. Then,

Area of kite = 12 d_{1}d_{2} square unit

Another way. Let a and b be the lengths of two unequal sides and θ be the angle included between them. Then

area of kite = ab sinθ square unit

## Perimeter of Kite

Sum of the lengths of all sides of a kite is called the perimeter of kite.

There are two pairs of equal sides of kite.

Let the length of the one pair of the equal side be a and the length of the another pair of the equal side be b.

If the perimeter of the kite is P,

P = (a + a+ b + b) unit

or, P = (2a + 2b) unit

∴ P = 2(a + b) unit

## Properties of Kite

- All interior angles add up to 360°.
- If all four sides of a kite are of equal length, it would be a rhombus.
- Only one diagonal divides the kite into two congruent isosceles triangle.
- If all four angles are equal measure, it must be a square.
- If the interior angles are equal to other, it forms a square.
- A kite is always orthogonal. That is, its two diagonals intersect at right angle or 90° to each other.
- Each pair of adjacent sides is distinct. More precisely, pairs cannot have a common side.
- One of the two diagonals divides the kite into two congruent triangles.
- If the all sides of a kite are equal in length, it forms a rhombus.
- One diagonal bisects (divides into two equal) a pair of opposite angles.
- Two distinct pairs of adjacent sides are of equal length.
- Two opposite angles formed by two unequal sides are equal.