Area of a Kite Formulas | List of Area of a Kite Formulas You Should Know - BYJUS

# Area of a Kite Formulas

A kite is a special type of quadrilateral in which both pairs of adjacent sides are congruent or equal. We will learn about the formula used to calculate the area of a kite and solve some examples to understand the formula for the area of a kite in a better manner....Read MoreRead Less

### What is a kite?

A closed polygon having four vertices, four sides and four angles is considered to be a quadrilateral. A kite is a quadrilateral in which each pair of the adjacent sides is congruent, but the opposite sides are not congruent. A rhombus can be considered a kite with all its four sides being congruent. Shown in the image is a kite with sides RQ, QP, RS and RS. The kite has two diagonals RP and QS represented by $$D_1$$ and $$D_2$$. ### Properties of a Kite

• Angles between the unequal sides of a kite are equal.
• View the kite as a pair of congruent triangles having a common base.
• The diagonals of a kite intersect such that the angle formed between them is 90 degrees.
• The longer diagonal is the perpendicular bisector of the shorter diagonal.
• A kite is symmetrical about its longer diagonal.
• The shorter diagonal divides the kite into two isosceles triangles.

### Formula for the Area of a kite

The area of the kite is half the product of its diagonals, that is A = $$\frac{1}{2}$$ x $$d_1$$ x $$d_2$$

In this formula, $$d_1$$ and $$d_2$$ are the lengths of the diagonals of the kite. ### Solved Examples

Example 1: The longer and shorter diagonals of a kite are 24 cm and 14 cm in a kite. What is the area of a kite?

Solution: As stated in the question,

Length of longer diagonal, $$d_1$$ = 24 cm

Length of shorter diagonal, $$d_2$$ = 14 cm

Area of a Kite, A = $$\frac{1}{2}$$ x $$d_1$$ x $$d_2$$

A = $$\frac{1}{2}$$ x 24 x 14

= 24 x 7

= 168  cm$$^2$$

So, the area of a kite is 168 square centimeters.

Example 2: The area of a kite is 420 square centimeters and one of its diagonals is 24 centimeter long. Find the length of the other diagonal.

Solution: The details given are,

Area of a kite, A = 420 cm²

Length of one diagonal, d$$_1$$ = 24 cm

Area of a Kite formula,

A = $$\frac{1}{2}$$ x $$d_1$$ x $$d_2$$

420 = $$\frac{1}{2}$$ x 24  x $$d_2$$

$$d_2$$ = $$\frac{840}{24}$$

$$d_2$$ = 35 cm

So, the other diagonal of the kite is 35 centimeters long.

Example 3: Sam, Cathay, Simon and Betty are four friends flying kites of the same size in a park. 13 inch and 16 inch are the lengths of the diagonals running across each kite. Determine the sum of areas of all the four kites.

Solution:

Lengths of diagonals are:

$$d_1$$ = 13 in

$$d_2$$ = 16 in

The area of each kite is:

A = $$\frac{1}{2}$$ x $$d_1$$ x $$d_2$$

= $$\frac{1}{2}$$ x 13 x 16

= 104 in$$^2$$

Since each kite is of the same size, therefore the total area of all the four kites is 4 × 104 = 416  in$$^2$$

Therefore, the area of the four kites is 416 square inches.