Given: klmn is a trapezoid, m∠k = 90° lm = 9, kn = 18, mn = 15, mh - altitude find: area of klmn

The answer is 162 square units. I got it right and I am in RSM. You can do this by:
1) You can find that KH is 9 because there is a rectangle.
2)You know that HN is 9 because KN = 18, and if KH is 9, then HN is 9. 18-9 = 9
3)Use Pythagorean theorem to find the hight of the triangle.
4)9^2 = 81, 15^2= 225, so 225-81=144, and the root of 144 is 12.
5) Now you know the height, so you can find the area of the rectangle.
6) 9*12 = 108 square units for the rectangle.
7) Find the area of the triangle. (9*12)÷2. 108÷2 = 54.
8) 54+108 = 162 square units.