Answer
$14=h$
Work Step by Step
To find the surface area, we must add the area of each side. The area of the top and bottom is $s\times s$, and the area of each side is $s\times h$. When we add these together we get:
$A=s\times s+s\times s+s\times h+s\times h+s\times h+s\times h$
Combine like terms.
$A=2(s\times s)+4(s\times h)$ or $A=2s^{2}+4sh$
We are solving for $h$, so we must get $h$ alone.
Subtract $2s^{2}$ from both sides.
$A-2s^{2}=4sh$
Divide by $4s$.
$\frac{A-2s^{2}}{4s}=h$
Plug in the given values: 760 for $A$ and 10 for $s$.
$\frac{760-2(10)^{2}}{4(10)}=h$
Solve.
$14=h$
Part c tells us that $s=h$. To solve this, substitute $s$ for $h$.
$A=2s^{2}+4s^{2}$
Add.
$A=6s^{2}$
