Surface area

Surface area is the total area of all the faces of a 3D shape. Unfold it into a net, find each face’s area and add them.

The idea: wrapping paper

Surface area is how much wrapping paper you would need to cover a shape exactly. It is measured in square units, like cm².

The easy way to find it is to unfold the shape into a flat net. Every face becomes a rectangle, triangle or circle whose area you already know (6.G.A.4).

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

topsidefrontsidebackbottom5 × 3, 5 × 2 and 3 × 2 faces, two of each
The net of a 5 × 3 × 2 box: two of each rectangle, 62 cm² in all.
curved side: 2πr × h
A cylinder unrolls into two circles and a rectangle 2πr long.

Surface area of a box

A box has 6 faces in 3 matching pairs: top and bottom, front and back, left and right.

SA = 2 × (l × w) + 2 × (l × h) + 2 × (w × h). A box 5 × 3 × 2 cm has SA = 2 × 15 + 2 × 10 + 2 × 6 = 62 cm².

Surface area of a cube

A cube has 6 equal square faces. If each edge is s, each face is s × s, so SA = 6 × s².

A cube with 4 cm edges has 6 × 16 = 96 cm². Doubling the edge makes the surface area 4 times as big.

Box explorer

The explorer shows the volume. Work out the surface area from the six faces too, and compare the two numbers.

Triangular prisms and pyramids

A triangular prism has 2 triangle ends and 3 rectangles. Find the area of each and add all five. The triangles use ½ × base × height.

A square pyramid has a square base and 4 matching triangles. SA = base area + 4 × triangle area.

Surface area of a cylinder

A cylinder’s net is two circles and one rectangle. The rectangle is as long as the circle’s circumference, 2πr, and as tall as the cylinder.

SA = 2πr² + 2πrh. A can with r = 3 cm and h = 10 cm has 2 × 3.14 × 9 + 2 × 3.14 × 3 × 10 = 56.52 + 188.4 = 244.92 cm².

Surface area or volume?

Surface area is the outside: paint, paper or material. Volume is the inside: how much it holds. They use different units, cm² and cm³.

Ask “am I covering it or filling it?” Covering means surface area; filling means volume.

Key words

A week of practice

Ten minutes a day is plenty. Short, regular practice beats one long session at the weekend.

If one day goes badly, repeat it rather than moving on. Each day builds on the one before.

Quiz: surface area

Picture the net. Add every face.

Where this fits: geometry step by step

  1. Lines, rays and line segments
  2. Types of angles
  3. Measuring angles with a protractor
  4. Angle relationships
  5. Polygons
  6. Types of triangles
  7. Angles in a triangle
  8. Quadrilaterals
  9. Symmetry
  10. Perimeter
  11. Area
  12. Area of composite shapes
  13. Area of triangles
  14. Area of parallelograms and trapezoids
  15. Parts of a circle
  16. Circumference and area of a circle
  17. Faces, edges and vertices
  18. Volume
  19. Surface area (this page)
  20. Volume of cylinders, cones and spheres
  21. The coordinate plane
  22. Transformations
  23. Pythagorean theorem

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “How many faces does a box have?” (6.)
  2. “Which faces match?” (Top and bottom, front and back, the two sides.)
  3. “What is the area of the top?”
  4. “And the front? And the side?”
  5. “Add them, then double. What do you get?”
  6. “Is that how much paint we need, or how much it holds?” (Paint.)

More worked examples

Example 1: Box 4 × 3 × 2 m

2 × 12 + 2 × 8 + 2 × 6 = 52 m².

Example 2: Cube, edge 5 in

6 × 25 = 150 in².

Example 3: Triangular prism

Two triangles of 6 cm² and rectangles of 20, 15 and 25 cm²: 12 + 60 = 72 cm².

Example 4: Cylinder r = 2, h = 5

2π × 4 + 2π × 2 × 5 = 8π + 20π = 28π ≈ 87.92.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. Box 2 × 2 × 2
  2. Box 3 × 2 × 1
  3. Box 6 × 4 × 3
  4. Cube, edge 3
  5. Cube, edge 10
  6. Box 5 × 5 × 2
  7. Cube with SA 96. Edge?
  8. Cylinder r = 1, h = 4 (in terms of π)
  9. Box 10 × 2 × 1
  10. Stretch: 8 cubes of edge 1 make a 2 × 2 × 2 cube. SA?
Show the answers
  1. 24
  2. 22
  3. 108
  4. 54
  5. 600
  6. 90
  7. 4
  8. 10π
  9. 64
  10. 24

Common mistakes

Counting only 3 facesAdds lw + lh + wh and stops.Fix: every face has a partner: double it.
Mixing up surface area and volumeMultiplies l × w × h.Fix: surface area adds face areas; volume multiplies three lengths.
Forgetting the cylinder’s circlesOnly finds the curved side.Fix: a closed can has a top and a bottom too.

How to teach it at home

Unfold a box

Open a cereal box flat and measure each panel. Add them up.

Wrap it

Estimate how much paper wraps a gift box, then check.

Cube builds

Build shapes from cubes and count the visible square faces.

By grade

More for each grade: Grade 6 math and the CBSE class 6 maths guide; Grade 7 math and the CBSE class 7 maths guide; Grade 8 math and the CBSE class 8 maths guide.

Worksheets and practice

Surface area worksheet, page 1

Surface area worksheet: printable PDF with an answer key. · Make a fresh test

Geometry practice · area and perimeter calculator · geometry for kids · area and perimeter chart · 3D shapes worksheet · faces, edges and vertices

Last reviewed

Questions parents ask

What is surface area?

The total area of all the faces of a 3D shape, measured in square units.

How do you find the surface area of a box?

SA = 2(lw + lh + wh): find the area of three different faces, add them and double.

What is the surface area of a cube?

6 × s², where s is the length of an edge.

How do you find the surface area of a cylinder?

Add the two circles and the curved side: 2πr² + 2πrh.

What is the difference between surface area and volume?

Surface area covers the outside (cm²); volume fills the inside (cm³).