Precalculus question

Question

Express the area of the shaded region below as a function of x. The dimensions in the figure are centimeters.

Answer 1

A = (Area of rectangle on bottom) + (Area of triangle on top) = (b*h_rectangle) + (0.5*b*h_triangle) (note: b is the same for the triangle and rectangle so it's x)

A = (3*x) + (0.5*x*h_triangle)

But how do we get h_triangle? Slope = rise over run = h/x = 5/6 so h = (5/6)*x so plug it in:

A = (3*x) + (.5*x*x*(5/6)) = (5/12)*x² + 3*x