Given

A
C
=
30
centimeters and
B
E
=
7
centimeters, determine the area of the kite.

The figure shows a kite with vertices labeled as Upper A, Upper B, Upper C, and Upper D. Dotted lines are drawn from Upper A to Upper C and from Upper B to Upper D, which intersect at a point labeled as Upper E. The length of the sides UpperWord AB and UpperWord AD is labeled as 10 centimeters, and the length of the sides UpperWord BC and UpperWord DC is labeled as 23 centimeters.

The area of the kite ABCD is
square centimeters.

1 answer

You could have just said:
The figure shows a kite with vertices labeled A, B, C, and D. Dotted lines are drawn from A to C and from B to D, which intersect at a point labeled as E. The length of the sides AB and AD is labeled as 10 centimeters, and the length of the sides BC and DC is labeled as 23 centimeters.

Look at triangle ABC, you know all the sides, so we could find angle B by the cosine law:
30^2 = 10^2 + 23^2 - 2(10)(23)cos B
I found B ≐ 126.1°

So now the area of ∆ABC = (1/2)(10)(23)sin 126.1°, which would be half the area of the kite