Area of a Kite

By definition, a kite's diagonals are perpendicular to one another.

The diagonals divide the kite into two big triangles – namely, $△ A B C$ and $△ A D C .$

The area of the kite equals the sum of the areas of the two triangles.

A_{A B C D} = A_{△ A B C} + A_{△ A D C}

By taking

\overline{A C}

as the base and

\overline{B E}

as the height, the area of

△ A B C

can be calculated as follows.

A_{△ A B C} = \frac{1}{2} A C \cdot B E

Similarly, the area of

△ A D C

can be found by taking

\overline{A C}

as the base and

\overline{E D}

as the height.

A_{△ A D C} = \frac{1}{2} A C \cdot E D

Next, substitute the areas of the triangles into the area of the kite.

A_{A B C D} = A_{△ A B C} + A_{△ A D C}

$A_{△ A B C} = \frac{1}{2} A C \cdot B E$ , $A_{△ A D C} = \frac{1}{2} A C \cdot E D$

A_{A B C D} = \frac{1}{2} A C \cdot B E + \frac{1}{2} A C \cdot E D

Factor out $\frac{1}{2} A C$

A_{A B C D} = \frac{1}{2} A C (B E + E D)

B E + E D

can be written as

B D .

A_{A B C D} = \frac{1}{2} A C (B E + E D)

$B E + E D = B D$

A_{A B C D} = \frac{1}{2} A C \cdot B D

$A C = d_{1}$ , $B D = d_{2}$

A_{A B C D} = \frac{1}{2} d_{1} d_{2}

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