Surface Area of Prisms

≈ 25 min

The surface area of a solid is the total area of all its faces — the amount of paper you would need to wrap it. Add up every face.

Cube (side $s$ ): six identical square faces, so surface area $= 6s^2$ .
Rectangular prism ( $l \times w \times h$ ): three pairs of matching rectangles, so surface area $= 2(lw + lh + wh)$ .

Worked example. A cube of side $4$ cm. Each face is $4 \times 4 = 16$ cm², and there are 6 faces, so surface area $= 6 \times 16 = 96$ cm².

A cube has side $10$ cm. Find its surface area, in cm².

The surface area of a cube with side $s$ is…

$s^3$

$6s^2$

$4s^2$

$6s$

A cube has side $4$ cm. Find its surface area, in cm².

A rectangular prism measures $5$ cm $\times$ $3$ cm $\times$ $2$ cm. Find its surface area, in cm².