Final answer:
The area of the right triangle is (10√(2)) cm^2.
Step-by-step explanation:
To find the area of a right triangle, we can use the formula A = 0.5 * base * height. In this case, the legs of the right triangle are given as (5√(2)) cm and (4√(2)) cm. We can use these lengths as the base and height of the triangle respectively. So, the area of the triangle is:
A = 0.5 * (5√(2)) cm * (4√(2)) cm
Simplifying, we get:
A = 10√(2) cm^2