The surface area of a prism is the sum of the areas of all the faces.
Finding surface area without drawing a net
A way to calculate the surface area of a prism is to calculate all the areas of the faces and add them up.
Exploration
This rectangular prism has dimensions of $8$8, $7$7 and $5$5.
The top and bottom faces would have the same area, so we can find this area and double it:
$2\times8\times7=112$2×8×7=112
The front and back would have the same area, so we can find this area and double it:
$2\times8\times5=80$2×8×5=80
The two sides would have the same area, so we can find this area and double it:
$2\times7\times5=70$2×7×5=70
Adding these areas will give us the total surface area for the prism:
$A=112+80+70=262\text{ units}^2$A=112+80+70=262 units2.
Practice questions
Question 1
Consider the following rectangular prism with a width, length and height of $5$5 m, $7$7 m and $15$15 m respectively. Find the surface area.
Question 2
Find the surface area of the triangular prism shown.
Question 3
Find the surface area of the figure shown.
Give your answer to the nearest two decimal places.
