Question

2. A right prism has a square base of edge a and altitude h, write the formula for the total surface area

Answer 1

Given the shape in the question the total surface area of a prism is given by:

$\begin{gathered} ph+2A \\ \text{where p=perimeter of the base} \\ h=\text{height} \\ A=\text{Area of the base} \end{gathered}$

Since the right prism is square based, then we have:

$\begin{gathered} \text{perimeter of a square = 4a where a is the edge of the square} \\ \text{Area of a square= a}^2 \end{gathered}$

Hence, the formula for the total surface area of the prism is given by:

$\begin{gathered} 4ah+2a^2 \\ \text{where a is the edge of the square and h is the height} \end{gathered}$