Kite Shape

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

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

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 d₁ are d₂. Then,

Area of kite = 12 d₁d₂ 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

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

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.

Each pair of equal sides are produced from a common vertex.