Question

The surface area (SA) of a rectangular prism can be determined by using the formula, where l = length, w = width, and h = height.

Answer 1

Explanation

We must solve for h the following equation:

$SA=2\cdot(l\cdot w+l\cdot h+h\cdot w).$

(1) We divide both sides by 2:

$l\cdot w+l\cdot h+h\cdot w=\frac{SA}{2}.$

(2) We pass the term lw on the left side as -lw on the right side:

$l\cdot h+h\cdot w=\frac{SA}{2}-l\cdot w.$

(3) We take h as a common factor on the left:

$h\cdot(l+w)=\frac{SA}{2}-l\cdot w.$

(4) Finally, we divide both sides by (l + w):

$h=\frac{\frac{SA}{2}-l\cdot w}{l+w}=\frac{SA}{2(l+w)}-\frac{lw}{l+w}.$Answer$h=\frac{SA}{2(l+w)}-\frac{lw}{l+w}$