area of a triangle...

Let's look at the area term.

243x^5 y^10

As you said, the fifth root of x^5 is x. Did you know that the fifth root of y^10 is y^2? Here's the fun part: 243 = 3^5, so the fifth root of 3^5 is 3. That means the area is

3xy^2

You already figured out the length is x. The area of a triangle is 1/2 base x height, so plugging in,

A = 1/2 B x H
3xy^2 = 1/2 x H
6y^2 = H