How To Find Area Of Kite Without Diagonals

A quadrilateral is a polygon which has four vertices and 4 sides enclosing iv angles. Kite is a special quadrilateral in which each pair of the consecutive sides is congruent, merely the opposite sides are not congruent. Rhombus is a kite with all the iv sides congruent. Properties of a Kite:

• Angles betwixt unequal sides are equal.
• A kite tin can be viewed as a pair of congruent triangles with a common base.
• Diagonals of a kite intersect each other at right angles.
• The longer diagonal is the perpendicular bisector of the shorter diagonal.
• A kite is symmetrical about its main diagonal.
• The shorter diagonal divides the kite into 2 isosceles triangles.

Formula for Expanse of a Quadrilateral

The diagonals of a kite are perpendicular. Area of a kite is given equally one-half of the product of the diagonals which is aforementioned equally that of a rhombus. Expanse of a kite can be expressed past the formula:

• Area of Kite = \(\frac{1}{ii}D_{ane}D_{ii}\)

D_one = long diagonal of kite

D₂= short diagonal of kite

Derivation for Expanse of a Kite:

Consider the surface area of the following kite PQRS.

Here the diagonals are PR and QS

Let diagonal PR =a and diagonal QS = b

Diagonals of a kite cut ane another at right angles equally shown by diagonal PR bisecting diagonal QS.

OQ = OS = \( \frac{OS}{2}=\frac{b}{2}\)

Surface area of the kite = Area of triangle PQR + Surface area of triangle PSR

Area of Triangle = \(\frac{1}{2}\;base \times summit\)

Hither, base = a and height = OQ = Os= b/ii

Area of triangle PQR = \(\frac{1}{2}\times a\times \frac{b}{ii}\)

Expanse of triangle PSR= \(\frac{1}{2}\times a\times \frac{b}{ii}\)

Area of the kite = \(\frac{ane}{2}\times a\times \frac{b}{2}\) + \(\frac{1}{2}\times a\times \frac{b}{2}\)

= \(\frac{ab}{iv}+\frac{ab}{4}\)

= \(\frac{2ab}{4}=\frac{1}{2}ab\)

Hence,

Expanse of the kite = \(\frac{one}{two}PR*QS\)= Half of the product of the diagonals

Note:

• If lengths of unequal sides are given, using Pythagoras theorem, the length of diagonals can be plant. The expanse of a kite can be calculated past using the lengths of its diagonals.

Solved Examples:

Example ane:Observe the area of kite whose long and short diagonals are 22 cm and 12cm respectively.

Solution: Given,

Length of longer diagonal, D₁= 22 cm

Length of shorter diagonal, D_two= 12 cm

Area of Kite =\(\frac{1}{2}D_{1}D_{two}\)

Area of kite = \(\frac{1}{two}\) 10 22 ten 12 = 132\(cm^{2}\)

Example 2:Surface area of a kite is 126 cm² and one of its diagonal is 21cm long. Find the length of the other diagonal.

Solution: Given,

Surface area of a kite =126 cm²

Length of one diagonal = 21 cm

Area of Kite =\(\frac{1}{2}D_{i}D_{2}\)

\(126 = \frac{1}{2}\times 21\times D_{two}\)

D_ii = 12cm

To solve more problems on the topic and for video lessons on kite and other quadrilaterals, download BYJU'S – The Learning App.

Source: https://byjus.com/area-of-a-kite-formula/

Posted by: novakdartakifinee.blogspot.com

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