☰ Year plan · Mathematics

Nets and surface area

Week 28 · Nets and surface area of cuboids, cubes, prisms and pyramids · 3 lessons
1

Nets and the surface area of a cuboid

Discover Mathematics P6: Term 2, Unit 13, Lessons 1–2
GoalUse a net to find the area of each face, and find the surface area of a cuboid.
New words
net · a flat pattern that folds up into a solidface · one flat side of a solidsurface area · the total area of all the faces of a solid
Explanation

A cuboid has six rectangular faces, in three equal pairs: top and bottom, front and back, left and right. If we unfold it we get a net, a flat shape with all six faces. The surface area is the sum of the areas of the six faces, measured in square units (cm² or m²). For a cuboid with length l, width w and height h, the top and bottom are l × w each, the front and back are l × h each, and the two sides are w × h each. So surface area = 2 × (l × w + l × h + w × h). In a drawing you see only three faces, so remember the three hidden faces that are equal to them.

ƒFormula
Surface area of a cuboid = 2 × (l × w + l × h + w × h)
Three pairs of equal faces.
Worked examples
15 cm²6 cm²6 cm²10 cm²10 cm²15 cm²
A cuboid is 5 cm long, 3 cm wide and 2 cm high. The net shows the six faces: 15 + 15 + 10 + 10 + 6 + 6 = 62. The surface area is 62 cm².
5 cm3 cm2 cm
With the formula: 2 × (5 × 3 + 5 × 2 + 3 × 2) = 2 × (15 + 10 + 6) = 2 × 31 = 62 cm². Same answer.
A box is 8 cm by 5 cm by 3 cm. Top and bottom: 2 × 40 = 80. Front and back: 2 × 24 = 48. Two sides: 2 × 15 = 30. Total 80 + 48 + 30 = 158 cm².
Class activity

Unfold a box. With a grown-up, carefully open a small cereal or medicine box along its edges and lay it flat. Measure the faces and find its surface area.

Practice
1
Find the surface area of a cuboid 7 cm by 3 cm by 2 cm.
2
Find the surface area of a cuboid 10 cm by 10 cm by 5 cm.
3
A carton is 20 cm by 15 cm by 10 cm. How much paper covers all six faces?
4
An open box (no lid) is 5 cm by 4 cm by 3 cm. Find the area of its five faces.
5
Why do we say the surface area is in cm² and not in cm³?