By definition, a kite's diagonals are to one another.
The diagonals divide the kite into two big – namely, △ ABC and △ ADC.
The area of the kite equals the sum of the .
A_(ABCD) = A_(△ ABC) + A_(△ ADC)
By taking AC as the base and BE as the height, the area of △ ABC can be calculated as follows.
A_(△ ABC) = 1/2AC* BE
Similarly, the area of △ ADC can be found by taking AC as the base and ED as the height.
A_(△ ADC) = 1/2AC* ED
Next, substitute the areas of the triangles into the area of the kite.
A_(ABCD) = A_(△ ABC) + A_(△ ADC)
A_(ABCD) = 1/2AC* BE + 1/2AC* ED
A_(ABCD) = 1/2AC(BE+ED)
By the , BE+ED can be written as BD.
A_(ABCD) = 1/2AC(BE+ED)
A_(ABCD) = 1/2AC* BD
A_(ABCD) = 1/2 d_1 d_2
