# A rectangular box has a square base and a closed top with dimensions x=length and h=height. How do you write the surface area in terms of x and h?

Jul 8, 2017

$2 {x}^{2} + 4 h x$

#### Explanation:

$\text{the cuboid has 6 faces}$

$\text{area of square base } = x \times x = {x}^{2}$

$\text{area of top is also square with area } = {x}^{2}$

$\text{the area of each of the other 4 faces } = h \times x = h x$

$\Rightarrow \text{surface area } = {x}^{2} + {x}^{2} + h x + h x + h x + h x$

$\textcolor{w h i t e}{\Rightarrow s u r f a c e a r e a} = 2 {x}^{2} + 4 h x$