Surface area of prisms

Nets and the total surface area of rectangular and triangular prisms.

Add the faces

The surface area is the total area of all the faces. Unfold the solid into its net and add up the areas.

Rectangular prism

$$SA = 2(lw + lh + wh)$$

Example 1●

Find the surface area of a box $10$ cm by $6$ cm by $4$ cm.

$2(60 + 40 + 24) = 2 \times 124$

$= 248$ cm²

Example 2●●

A triangular prism has a right-angled triangle face with sides $3$, $4$ and $5$ cm, and length $10$ cm. Find its surface area.

Two triangles: $2 \times \tfrac{1}{2} \times 3 \times 4 = 12$ cm².

Three rectangles: $10 \times (3 + 4 + 5) = 120$ cm².

$SA = 132$ cm²

Flashcards

Surface area

Total area of all faces.

Cube of side s

$6s^2$

Sides of a prism

length × perimeter of the end

Practice

Surface area of a $10 \times 6 \times 4$ cm box?
Surface area of the triangular prism in Example 2?
Surface area of a cube with side $5$ cm?
Surface area of a $5 \times 4 \times 3$ box?
How many faces does a rectangular prism have?
A cube has surface area $96$ cm². Find its side length.
An open box (no lid) is $10 \times 6 \times 4$ cm. Find its outside surface area.
A prism is $15$ cm long and its end has perimeter $12$ cm. Find the area of its rectangular faces.