Question

The surface area of a rectangular prism is 442 square feet. The length is 11 feet, and the height is 8 feet. What is the width of the prism?
I need an explanation please on how to work this problem.

Answer 1

There are 6 surfaces on a rectangular prism . 3 pairs of equal area.

Surface area  2wl + 2hw + 2 hl     where h = height, w = width,  l = length.

So inserting the given values:-

442 = 2*w*11 + 2 *8* w + 2*8*11

442 = 22w  + 16w + 176

38w =  442-176 = 266

w =  7

width = 7 feet

Answer 2

Formula for the surface area of a rectangular prism is S=2ab + 2bc + 2ac (a-lenght,b-width,c-height).
We need to calculate b (width).
S=442 ft^2
a=11 ft
c=8ft
------------------
b=?

S=2ab + 2bc + 2ac
S=2b(a+c) + 2ac
2b(a+c)=S - 2ac
b=(S - 2ac)/(2(a+c))
b=(442 - 2×11×8)/(2×(11+8))
b=(442 - 176)/(2×19)
b=266/38
b=7 ft