We are given the surface area S = 432in^2, height h = 6in, and width w = 12in. of a rectangular prism. We want to find its volume. To do so, we can use the following formula, where B is the area of the base and h is the height.
V=Bh
Note, the base is a rectangle, so we can calculate its area using the formula for area of a rectangle.
B = l wWe know w, but we do not know l. We do, however, know the surface area of the prism. It can be calculated using the formula for the surface area of a prism, where P is the perimeter of the base, h is the height, and B is the area of the base.
S = 2B + Ph
Let's recall the formula for the perimeter of a rectangle.
P = 2(l+w)
We can substitute the formulas for the perimeter and area of a rectangle into the formula for the surface area of the prism.
S = 2B + Ph ↔ S = 2l w + 2(l + w)h
Now we can substitute 432 for S, 6 for h, and 12 for w in order to find l.
