Question

Find the area of the figure below. Show all work for each step. Work should include explanations in words detailing how you simplify each specific radical. Take your time and be thorough. Include units in the final answer. Use radicals in your work and not decimals!
image: Rectangle with a base of (7√3+ 5√6)
Height (-2√3+ 3√6)

Answer 1

I wanted to check to see if I was right I used the foil method
(7√3+ 5√6) x (-2√3+ 3√6)
-14√9 + -21√18 + -10√18 + 15√36
-14x3 + 11√18 + 15x6
-42+11√18+90
48 + 11√18in

Answer 2

so far, so good, but note that √18 = 3√2