Area is the number of square units needed to cover a surface or figure and relates to a 2D object. The surface area is the area covering a 3D object.
Surface area has lots of applications. Here are some examples:
Many objects have complex shapes to increase their surface area: the inside of your lungs, intestines, and brain; air purifiers, or radiators.
We will start by looking at how to find the surface area of a rectangular prism.
Rectangular prisms have three pairs of congruent faces. We can see below how we could break the rectangular prism above into three pairs of congruent rectangles. To find the total surface area, we must add up the area of all of the faces.
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Have a look at this interactive to see how to unfold rectangular prisms.
Consider the questions below.
When needing to calculate the surface area (SA) of a prism we need to add up the areas of individual faces. Make sure not to miss any faces but also try to look for clever methods, like using the fact that $2$2 faces might have the same area.
While we are just looking at rectangular prisms for now, the concept below will help us in future lessons too.
$\text{Surface area of a prism }=\text{Sum of areas of faces}$Surface area of a prism =Sum of areas of faces
If we are just looking at a rectangular prism, we can use a formula instead of adding up all $6$6 faces separately.
As we saw with the applet above, there are three pairs of congruent rectangles.
Since there are two of each of these rectangles we get the formula below.
$\text{S.A. }=2lw+2lh+2wh$S.A. =2lw+2lh+2wh
Consider the following cube with a side length equal to $6$6 cm. Find the total surface area.
Consider the following rectangular prism with length, width, and height, equal to $12$12 m, $6$6 m, and $4$4 m, respectively.
Find the surface area of the prism.
What is the surface area of a cube with side length $4$4 cm?