Find the area of the triangle if 8 and 12 are a leg and hypotenuse.

This is a right triangle; In a right triangle the base and the height are the legs.
We have to calculate the other leg.
Pythagoras Theroem:
leg₁²+leg₂²=hypotenuse²

Data:
leg₁=8
hypotenuse=12

Therefore:
8²+leg₂²=12²
64+leg₂²=144
leg₂²=144-64
leg₂²=80
leg₂=√80=4√5

Area of a triangle=(base * height) /2=(leg₁*leg₂)/2=(8)(4√5)/2=16√5

the area of this triangle would be 16√5 u²