Surface area of cuboids

The Maths Habit

1 Work out the area of the rectangle.

5 cm3 cm
15 cm2

2 Work out the area of the rectangle.

4 cm2 cm
8 cm2

3 What is 18 × 2?

36

This box is opened out flat. How many faces does it have? Which faces match?

6 faces, in 3 matching pairs: top and bottom, front and back, the two sides.

Face
A flat side of a 3D shape.
Edge
Where two faces meet.
Net
A 3D shape opened out flat.
Surface area
The total area of all the faces.

Which two lengths make the front face?

6 cm3 cm4 cm6 cm and 3 cm

Which two lengths make the top face?

5 cm2 cm4 cm5 cm and 4 cm

lengthheightwidth
  1. One face: top, front and side.Multiply its two lengths.
  2. Double.Matching faces come in pairs.
  3. Add the three pairs.Surface area is in cm².
1 One face2 Double
toplength×width=× 2 =
frontlength×height=× 2 =
sidewidth×height=× 2 =
3 Add  totalcm²

Work out the surface area.

6 cm3 cm2 cm
1 One face2 Double
top6×2=12× 2 =24
front6×3=18× 2 =36
side2×3=6× 2 =12
3 Add  total72cm²

Work out the surface area.

8 cm2 cm3 cm
1 One face2 Double
top8×3=24× 2 =48
front8×2=16× 2 =32
side3×2=6× 2 =12
3 Add  total92cm²

Work out the surface area.

6 cm3 cm2 cm
1 One face2 Double
top6×2=12× 2 =24
front6×3=18× 2 =36
side2×3=6× 2 =12
3 Add  total72cm²

Work out the surface area.

10 cm4 cm2 cm
1One face top, front, side2Double faces come in pairs3Add the three pairs
1 One face2 Double
top10×2=20× 2 =40
front10×4=40× 2 =80
side2×4=8× 2 =16
3 Add  total136cm²

Work out the surface area.

6 cm3 cm2 cm
1 One face2 Double
top6×2=12× 2 =24
front6×3=18× 2 =36
side2×3=6× 2 =12
3 Add  total72cm²

Work out the surface area.

5 cm2 cm5 cm
1One face top, front, side2Double faces come in pairs3Add the three pairs
1 One face2 Double
top5×5=25× 2 =50
front5×2=10× 2 =20
side5×2=10× 2 =20
3 Add  total90cm²

Work out the surface area.

6 cm3 cm2 cm
1 One face2 Double
top6×2=12× 2 =24
front6×3=18× 2 =36
side2×3=6× 2 =12
3 Add  total72cm²

Work out the surface area.

7 cm4 cm3 cm
1One face top, front, side2Double faces come in pairs3Add the three pairs
1 One face2 Double
top7×3=21× 2 =42
front7×4=28× 2 =56
side3×4=12× 2 =24
3 Add  total122cm²

Work out the surface area of each cuboid.

14 cm3 cm3 cm
1 One face2 Double
top4×3=12× 2 =24
front4×3=12× 2 =24
side3×3=9× 2 =18
3 Add  total66cm²
210 cm2 cm5 cm
1 One face2 Double
top10×5=50× 2 =100
front10×2=20× 2 =40
side5×2=10× 2 =20
3 Add  total160cm²
37 cm2 cm2 cm
1 One face2 Double
top7×2=14× 2 =28
front7×2=14× 2 =28
side2×2=4× 2 =8
3 Add  total64cm²
1One face top, front, side2Double faces come in pairs3Add the three pairs

4 cm4 cm4 cm
  1. A cube has 6 faces.Every face is the same square.
  2. Use the same frame.Every row is the same.
  3. One face, double, add.16 × 2 = 32, then 32 + 32 + 32 = 96 cm².

Work out the surface area.

2 cm2 cm2 cm
1 One face2 Double
top2×2=4× 2 =8
front2×2=4× 2 =8
side2×2=4× 2 =8
3 Add  total24cm²

Work out the surface area.

5 cm5 cm5 cm
1 One face2 Double
top5×5=25× 2 =50
front5×5=25× 2 =50
side5×5=25× 2 =50
3 Add  total150cm²

Work out the surface area.

2 cm2 cm2 cm
1 One face2 Double
top2×2=4× 2 =8
front2×2=4× 2 =8
side2×2=4× 2 =8
3 Add  total24cm²

Work out the surface area.

10 cm10 cm10 cm
1One face top, front, side2Double faces come in pairs3Add the three pairs
1 One face2 Double
top10×10=100× 2 =200
front10×10=100× 2 =200
side10×10=100× 2 =200
3 Add  total600cm²

Work out the surface area.

2 cm2 cm2 cm
1 One face2 Double
top2×2=4× 2 =8
front2×2=4× 2 =8
side2×2=4× 2 =8
3 Add  total24cm²

Work out the surface area.

6 cm6 cm6 cm
1One face top, front, side2Double faces come in pairs3Add the three pairs
1 One face2 Double
top6×6=36× 2 =72
front6×6=36× 2 =72
side6×6=36× 2 =72
3 Add  total216cm²

Work out the surface area.

2 cm2 cm2 cm
1 One face2 Double
top2×2=4× 2 =8
front2×2=4× 2 =8
side2×2=4× 2 =8
3 Add  total24cm²

Work out the surface area.

1 cm1 cm1 cm
1One face top, front, side2Double faces come in pairs3Add the three pairs
1 One face2 Double
top1×1=1× 2 =2
front1×1=1× 2 =2
side1×1=1× 2 =2
3 Add  total6cm²

Work out the surface area of each cube.

13 cm3 cm3 cm
1 One face2 Double
top3×3=9× 2 =18
front3×3=9× 2 =18
side3×3=9× 2 =18
3 Add  total54cm²
24 cm4 cm4 cm
1 One face2 Double
top4×4=16× 2 =32
front4×4=16× 2 =32
side4×4=16× 2 =32
3 Add  total96cm²
38 cm8 cm8 cm
1 One face2 Double
top8×8=64× 2 =128
front8×8=64× 2 =128
side8×8=64× 2 =128
3 Add  total384cm²
1One face top, front, side2Double faces come in pairs3Add the three pairs

Is the surface area right? Thumbs up or thumbs down.

A6 cm2 cm5 cmSurface area = 104 cm2Right
B4 cm2 cm4 cmSurface area = 32 cm2Wrong: 64 cm2
C3 cm2 cm2 cmSurface area = 12 cm2Wrong: 32 cm2
D2 cm2 cm2 cmSurface area = 24 cm2Right

Surface area of cuboids worksheet, page 1

Surface area of cuboids worksheet, page 2

Answer sheet

  1. A box has no lid. It is 5 cm long, 4 cm wide and 2 cm tall. Work out the area of its outside.

    56 cm2

  2. A cube has a surface area of 54 cm². How long is each edge?

    3 cm

  3. Two cubes with 2 cm edges are glued face to face. Work out the surface area of the new shape.

    40 cm2

  1. Work out the surface area. 1top5×2=102× 2 =20front5×2=10× 2 =20side2×2=4× 2 =8

    3Add: total = 48 cm2
    5 cm2 cm2 cm

  2. Work out the surface area. 1top7×3=212× 2 =42front7×2=14× 2 =28side3×2=6× 2 =12

    3Add: total = 82 cm2
    7 cm2 cm3 cm

  3. Work out the surface area.

    Surface area = 124 cm2
    9 cm4 cm2 cm
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