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Geometry & Measures · Foundation & Higher

Surface area

Surface area is the total area of all faces of a 3D shape. You calculate the area of each face separately and add them together.

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Key facts to remember

  • 1Surface area of a cuboid = 2(lw + lh + wh).
  • 2Surface area of a cylinder = 2πr² + 2πrh (two circular ends + curved surface).
  • 3Surface area of a triangular prism = sum of the two triangular faces + three rectangular faces.
  • 4Nets help visualise surface area — unfold the shape and find the total area.
  • 5Units are always square units (cm², m²).
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Formulas

Cuboid
SA = 2(lw + lh + wh)
Cylinder
SA = 2πr² + 2πrh

Curved surface = 2πrh; each end = πr²

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Worked examples

Example 1

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

Working

  1. Top and bottom: 2 × (5 × 3) = 30
  2. Front and back: 2 × (5 × 4) = 40
  3. Left and right sides: 2 × (3 × 4) = 24
  4. Total = 30 + 40 + 24 = 94 cm²
Answer94 cm²
Example 2

Find the surface area of a cylinder with radius 4 cm and height 10 cm. Give your answer in terms of π.

Working

  1. Two circular ends: 2 × π × 4² = 32π
  2. Curved surface: 2 × π × 4 × 10 = 80π
  3. Total = 32π + 80π = 112π cm²
Answer112π cm²
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Common mistakes

✗Forgetting pairs of faces — each face of a cuboid appears twice (top/bottom, front/back, sides).
✗Confusing surface area with volume.
✗Only finding the curved surface of a cylinder and forgetting the two circular ends.
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Exam tips

✓Sketch the net of the shape to identify all faces before calculating.
✓Check you have the right number of faces — a cuboid has 6, a triangular prism has 5.

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