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The area of a kite is one-half the product of the lengths of the diagonals.
The following is the equation for the area of kite ABCD.
A = 1/2AC* BD ⇔ A=1/2 d_1 d_2
The diagonals divide the kite into two big triangles – namely, △ ABC and △ ADC.
The area of the kite equals the sum of the areas of the two triangles. 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_(△ ABC)= 1/2AC* BE, A_(△ ADC)= 1/2AC* ED
Factor out 1/2AC
By the Segment Addition Postulate, BE+ED can be written as BD.
BE+ED= BD
AC= d_1, BD= d_2