Developing the formula for the Surface Area of a Prism

A Prism

You can think of surface area as the area of the outside covering a 3-dimensional object.

For instance, the amount of cardboard required for a cereal box.

A PrismConsider the following diagram. The diagram is a rectangular prism.

Top and Bottom are Orange.

Front and Back are Yellow.

The 2 sides are Green.

The NetIf we unfold the prism, you will see the prism unfolded, or the net.

The Net

Compare how the sides match up:

Finding the Formula

To determine the formula for finding the surface area of a rectangular prism, all we need to do is look at the shapes left over in the net:

Finding the Formula

L

h

w

h

Look at the rectangles that are left.

We need to find the area of each rectangle to find the surface area.

w

L

L

L

w

h h

Finding the Formula

So, we have:

SA = 2(Orange) + 2(Green) + 2(Yellow)

SA = 2(Lw) + 2(wh) + 2(Lh)

the formula for the surface area of a prism must be:

SA = 2Lw + 2wh + 2Lh

We will use this for the rest of the unit.