Surface Area Examples in Math

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

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 the faces or surfaces that enclose a three-dimensional object, measured in square units.

How much wrapping paper would you need to completely cover every face of a gift box?

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 is the 'skin' of a 3D shape—2D measurement of a 3D object's exterior.

Common stuck point: Surface area covers the outside (square units); volume fills the inside (cubic units)—never mix them.

Sense of Study hint: Try imagining you could unfold the 3D shape flat (a net). Then add up the area of every flat piece.

Worked Examples

Example 1

easy
Find the surface area of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm.

Solution

  1. 1
    A rectangular prism has 6 faces forming 3 pairs of identical rectangles. Label the pairs: l \times w (top/bottom), l \times h (front/back), w \times h (left/right). Total: SA = 2(lw + lh + wh).
  2. 2
    Substitute l = 4 cm, w = 3 cm, h = 5 cm: calculate each pair — lw = 12, lh = 20, wh = 15.
  3. 3
    Compute: SA = 2(12 + 20 + 15) = 2(47) = 94 cm². Each pair of faces contributes twice to the total surface.

Answer

SA = 94 \text{ cm}^2
Surface area is the total area of all faces of a 3D shape. For a rectangular prism, compute the area of each distinct face and double it (since opposite faces are congruent).

Example 2

medium
Find the surface area of a cylinder with radius 4 cm and height 7 cm. Leave your answer in terms of \pi.

Practice Problems

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

Example 1

easy
Find the surface area of a cube with side length 6 cm.

Example 2

medium
A cube has surface area 150 cm². Find the length of one edge.
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Background Knowledge

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

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