How do I find the area of this kite?

85 square units

Step-by-step explanation:

The area of a kite is half of the product of the diagonals.

The left half of the horizontal diagonal is labeled 5, so the entire horizontal diagonal measures 10.

Now we need to find the length of the vertical diagonal.

The vertical diagonal is made up of two segments. Each segment is a leg in a right triangle. We can use the Pythagorean theorem twice to find the lengths of the two segments of the vertical diagonal.

Upper vertical segment:

a^2 + b^2 = c^2

5^2 + x^2 = [5sqrt(2)]^2

25 + x^2 = 50

x^2 = 25

x = 5

The upper segment of the vertical diagonal has length 5.

Lower vertical segment:

a^2 + b^2 = c^2

5^2 + x^2 = 13^2

25 + x^2 = 169

x^2 = 144

x = 12

The lower segment of the vertical diagonal has length 12.

The length of the vertical diagonal is the sum of the lengths of the two vertical segments:

5 + 12 = 17

The diagonals of the kite measure 1`0 and 17.

area = d1 * d2/2

area = 10 * 17/2 = 170/2 = 85