Area of kite is the space enclosed by a kite. A kite is a quadrilateral in which two pairs of surrounding sides space equal. The elements of a kite room its 4 angles, that 4 sides, and also 2 diagonals. In this article, we will emphasis on the area the a kite and its formula.

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1.What Is the Area the a Kite?
2.Area of a kite Formula
3.Derivation the the Area of dragon Formula
4.FAQ's on Area that a Kite

The area of a kite can be defined as the quantity of an are enclosed or encompassed by a dragon in a two-dimensional plane. Like a square, and a rhombus, a kite does not have actually all four sides equal. The area the a kite is constantly expressed in regards to units2 because that example, in2, cm2, m2, etc. Let united state learn around the area that a dragon formula in our next section.


The area that a dragon is half the product of the lengths that its diagonals. The formula to determine the area of a kite is: Area = \(\dfrac12\times d_1\times d_2\). Below \(d_1\) and \(d_2\) room long and also short diagonals that a kite.The area of dragon ABCD given listed below is ½ × AC × BD.

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BD = lengthy diagonal and also AC = brief diagonal


Consider a dragon ABCD as shown above.

Assume the lengths of the diagonals that ABCD to it is in AC = p, BD = q

We understand that the much longer diagonal the a kite bisects the shorter diagonal at right angles, i.e., BD bisects AC and also ∠AOB = 90°, ∠BOC = 90°.

Therefore,

AO = OC = AC/2 = p/2

Area of dragon ABCD = Area that ΔABD + Area of ΔBCD...(1)

We understand that,

Area of a triangle = ½ × base × Height

Now, we will calculate the locations of triangles ABD and BCD

Area that ΔABD = ½ × AO × BD = ½ × p/2 × q = (pq)/4

Area the ΔBCD = ½ × OC × BD = ½ × p/2 × q = (pq)/4

Therefore, using (1)

Area of dragon ABCD = (pq)/4 + (pq)/4= (pq)/2Substituting the values of p and qArea of a kite = ½ × AC × BD

Important Notes

A kite has two bag of surrounding equal sides.

Example 1: 4 friends room flying kites of the exact same size in a park. The lengths the diagonals of every kite are 12 in and also 15 in. Recognize the amount of locations of every the 4 kites.

Solution:

Lengths of diagonals are:

\(d_1\) =12in

\(d_2\) =15in

The area the each kite is:

A = \(\dfrac12\times d_1\times d_2\)= ½ × 12 × 15= 90 in2

Since each dragon is the the same size, as such the total area of every the 4 kites is 4 × 90 = 360in2.Therefore the area the the 4 kites is 360in2


Example 2: Kate wants to offer a kite-shaped coco box to her friend. She desires to dough a picture of herself v her girlfriend to cover the top of the box. Determine the area the the height of the box if the diagonals the the lid of the box room 9 in and also 12 in.

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Solution:

\(d_1\) =9in

\(d_2\) =12in

Since package is kite-shaped, because of this the area the the optimal of package is:

A = \(\dfrac12\times d_1\times d_2\)= ½ × 9 × 12Therefore, the area that the top of package is 54in2


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