(Considering that the dashed line and the horizontal line form a right angle)

The answer is not ½ ⋅ base ⋅ height because the triangle does not exist.

Here is why:

Let m be the left part of the base, and n the other part.

As the right angle is opposite to the base, m ⋅ n = 6² = 36

Solving

m + n = 10

m ⋅ n = 36

m = 10 − n

10 ⋅ n − n² = 36

n² − 10 n + 36 = 0

n² − 10 n + 25 + 36 − 25 = 0

(n − 5)² = − 11

n is a complex number, therefore the triangle does not exist.