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Answer:

Since ABCD is a kite, we know that AE = CE and AD = CD.

Therefore, 5x + 1 = x + 4

Solving for x, we get x = 1

Substituting x = 1, we get:

AE = 5(1) + 1 = 6 and CE = 1 + 4 = 5.

AB = 4(1) + 4 = 8 and BC = AB = 8.

AD = 9(1) = 9 and CD = 9.

Using the formula for the area of a kite (A = 1/2 * d1 * d2), we need to find the diagonals of the kite.

Since AE = CE, we can combine them to get one diagonal: AC.

AC = 2AE = 2(6) = 12.

To find BD, we can use the Pythagorean theorem since we know AB and BC:

BD^2 = AB^2 + BC^2 = 8^2 + 8^2 = 128

BD = √128 = 8√2

Now we can find the area:

A = 1/2 * AC * BD = 1/2 * 12 * 8√2 = 48√2.

Step-by-step explanation:

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