We can see from the information given about the lines that everything that looks like a right angle actually is a right angle, and that all three triangles must be right isosceles triangles. Since we've been told that the areas of all three are 18, we can say that bh/2 = 18. Then we know that bh = 36. Since a right isosceles triangle has a base and height that are identical, we can see that both the base and height must be 6.

It's mandatory to know the side ratios of right isosceles triangles, since we'll be encountering them constantly. The side ratios are 1-1-√2. Since each of these triangles have sides of 6 and 6, we know the hypotenuse must equal 6√2.

Finally, since the perimeter of the whole figure is basically the perimeters of all three identical triangles, we can figure out the perimeter of one triangle and multiply by 3. Since the sides of one triangle are in the ratio of 6-6-6√2, the perimeter of one triangle is thus 12 + 6√2. If we multiply this by 3 we get 36 + 18√2, or answer choice B.