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Perimeter of Kite – Definition, Formula & Examples

perimeter of kite

Perimeter and area are the two important measurements In mathematics. Perimeter is a measurement of the distance around a shape and area gives us an idea of how much surface the shape covers. These help you to quantify physical space and also provide a foundation for more advanced mathematics found in algebra, trigonometry, and calculus.

Let’s learn about the perimeter of kite, its formula, and its properties.

Kite – A 2D Plane Figure

A kite is a 2D shape in which two pairs of adjacent sides are of equal length. No pair of sides in a kite are parallel but one pair of opposite angles are equal. The two diagonals are unequal and intersect at right angles. The longer diagonal of a kite bisects the shorter one.

perimeter of kite

Properties of Kite

Following are the characteristic features of a kite

  • A kite has two pairs of adjacent equal sides. Here, $AB = BC$ and $CD = DA$
  • It has one pair of opposite angles (obtuse) that are equal. Here, $\angle A = \angle C$
  • The longer diagonal bisects the shorter one. Here, the diagonal $AB$, $AO = OC$
  • The shorter diagonal forms two isosceles triangles. Here, diagonal $AC$ forms two isosceles triangles: $\triangle ACD$ and $\triangle ABC$. $AD = CD$ and $AB = BC$ in two isosceles triangles
  • The longer diagonal forms two congruent triangles. Here, diagonal $BD$ forms two congruent triangles – $\triangle ABD$ and $\triangle BCD$ by $SSS$ criteria. 
  • The diagonals are perpendicular to each other. Here, $BD \perp AC$
  • The longer diagonal bisects the pair of opposite angles. Here, $\angle ADB = \angle BDC$, and $\angle ABD = \angle DBC$

What is the Perimeter of a Kite – Perimeter of Kite Formula

The perimeter of a kite is the sum of all the sides of the kite. You can calculate the perimeter by adding the sides of each pair. 

If the sides of a kite are $a$, $b$, $a$ and $b$, then perimeter of kite is given by $P = a + b + a + b = 2a + 2b = 2\left(a + b \right)$.

perimeter of kite

Examples

Ex 1: A kite is having its equal sides of $4 cm$ and $5 cm$ respectively. Find its perimeter.

The two equal sides are $a = 4 cm$ and $b = 5 cm$

Therefore, perimeter of kite = $2\left(a + b \right) = 2\left(4 + 5 \right) = 2 \times 9 = 18 in$.

Ex 2: The perimeter of a kite is $54 in$. If one pair of equal sides are of length $12 in$, then find the length of the other two equal sides.

The perimeter of kite $P = 54 in$

Length of one pair of equal sides $a = 12 in$

Let the length of the second pair of equal sides be $b$

Therefore, $P = 2\left(a + b \right) => 54 = 2\left(12 + b \right) => \frac {54}{2} =12 + b  => 27 = 12 + b => b = 27 – 12 = 15 in$.

Ex 3: The sides of a kite are in the ratio of $3:5$. If the side smaller among them is $24 in$, find its perimeter.

Let the length of two pairs of equal sides be $3x$ and $5x$.

Therefore, $3x = 24 => x = \frac {24}{3} => x = 8$.

Thus, length of longer pair of sides = $5 \times 8 = 40$.

Therefore, $a = 24$ and $b = 40$.

Perimeter of kite = $2\left(a + b \right) = 2\left(24 + 40 \right) = 2 \times 64 = 128 in$.

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Practice Problems

  1. Find the perimeter of a kite having its pairs of equal sides as
    • $5 cm$ and $12 cm$
    • $6 m$ and $8 m$
  2. For the following ratio of shorter side and longer side, find the perimeter of a kite
    • $3:5$, perimeter = $30 m$
    • $5:12$, perimeter = $68 mm$

FAQs

How do you find the perimeter of a kite?

A kite is a 2-dimensional figure consisting of two pairs of triangles of equal size. The sum of all the sides of the kite is called the perimeter of the kite. This distance may be calculated by adding the sides of each pair.

What is the formula for the area of a kite?

The area of a kite is $\frac{1}{2} \times d_{1} \times d_{2}$, where $d_{1}$ and $d_{2}$ are the length of the two diagonals.

Conclusion

A kite is a 2D shape where there are two pairs of equal adjacent sides, where one of the pairs is smaller than the other pair of adjacent sides. The perimeter of a kite is given by the formula $2\left(a + b \right)$, where $a$ and $b$ are the lengths of smaller and longer pairs of adjacent sides.

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