Surface Area of a Prism Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Surface Area of a Prism.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The total area of all faces of a prism, found by adding the areas of the two bases and all lateral (side) faces.

Imagine unfolding a cereal box and laying it flat—you get a net of six rectangles. The surface area is the total area of that flattened cardboard. For any prism, you always have two identical bases plus a 'belt' of rectangles wrapped around the middle.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Surface area of a prism = 2 bases + lateral area. The lateral area is the base perimeter times the height.

Common stuck point: Don't forget there are TWO bases. The lateral area is like a rectangular 'wrapper' whose width is the base perimeter.

Worked Examples

Example 1

easy
A rectangular prism (box) has length 5 cm, width 3 cm, and height 4 cm. Find its surface area.

Solution

  1. 1
    Step 1: For a rectangular prism, the surface area formula is SA = 2(lw + lh + wh), which fits the general form SA = 2B + Ph for a rectangular base.
  2. 2
    Step 2: Calculate each face pair: lw = 5 \times 3 = 15; lh = 5 \times 4 = 20; wh = 3 \times 4 = 12.
  3. 3
    Step 3: SA = 2(15 + 20 + 12) = 2 \times 47 = 94 cm².

Answer

SA = 94 cm².
The surface area of a rectangular prism consists of 3 pairs of congruent rectangles. Each pair has area equal to the product of two dimensions. The total is twice the sum of the three face areas. This is the most common prism in everyday life (cereal boxes, shipping boxes, etc.).

Example 2

medium
A triangular prism has a triangular base with base 6 cm and height 4 cm, and the prism's length is 10 cm. The three sides of the triangular base are 5, 5, and 6 cm. Find the total surface area.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A cube has side length 7 cm. Find its surface area.

Example 2

hard
A prism has a regular hexagonal base with side length 4 cm. The prism has height 10 cm. Find the surface area. (Area of regular hexagon with side s: A = \frac{3\sqrt{3}}{2}s^2.)
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Background Knowledge

These ideas may be useful before you work through the harder examples.

areasurface area