Kite
A Kite is a flat shape with straight sides. It has two pairs of equal length with adjacent sides.
Properties of a kite
- A kite has two pairs of sides.
- Two pairs are equal in length and both sides are adjacent.
- Where two pairs of sides meet the angles are equal.
- Diagonals cross at right angles.
Area of a Kite
Space enclosed by a kite is called its area. A kite has 4 angles, 4 sides, and 2 diagonals. The area of the square is always expressed in square units like
Area of a kite = [katex] \frac12\;D_1D_2[/katex]
How to derive a formula to find the area of a kite
We want to find the area of a kite[katex] ABCD[/katex]
The length of the diagonals of ABCD to be [katex] AC=p [/katex] and [katex] BD = q[/katex]
Longer diagonal bisects the shorter diagonal at a right angle that is BD bisect AC and [katex] ∠AOB=90°[/katex] , [katex] ∠BOC=90° [/katex]
So,
[katex] AO=OC=AC/2 =p/2[/katex]
Area of kite = [katex] Area of triangle ABD + Area of triangle BCD…….(1)[/katex]
Area of triangle =[katex] ½ (base)(height)[/katex]
Area of triangle ABD =[katex] ½ (AO)(BD)[/katex]
=[katex] ½ (p/2) (q)[/katex]
=[katex] (pq)/4[/katex]
Area of triangle BCD =[katex] ½ (OC)(BD)[/katex]
=[katex] ½ (p/2) (q)[/katex]
=[katex] (pq)/4[/katex]
By using eq. 1
Area of kite ABCD= [katex] (pq)/4+(pq)/4[/katex]
=[katex] (pq)/2[/katex]
As we know
[katex] p=AC ,q = BD[/katex]
Area of kite =[katex] ½ (AC)(BD)[/katex]