Geometry · Surface area & volume · 4.2

Surface area of a box.

Surface area is the total area of all the faces — the wrapping paper. A box has three pairs of matching faces, so SA = 2(lw + lh + wh). A 3 × 4 × 5 box: 2(12 + 15 + 20) = 94.

01 / THE IDEA

See it work.

The figure

See the shape.

345

Watch the method

Surface area of a box

Surface area of a box = 2(lw + lh + wh).

1 / 2
1

Surface area of a box

Add the areas of all six faces — they come in three matching pairs.

2(lw+lh+wh)2(lw + lh + wh)
2

Substitute

Compute each face pair, then double the sum.

2(3⋅4+3⋅5+4⋅5)=942(3\cdot4+3\cdot5+4\cdot5) = 94
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Find the measure.

Type the number — units optional.

streak 0
best 0

…

— / WHY IT WORKS

The idea underneath.

Wrap the box

Each pair of opposite faces matches, so compute three and double.

Why it works

Unfold the box flat.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Surface area of a 3×8×3 box?

1

Surface area of a box

Add the areas of all six faces — they come in three matching pairs. 2(lw + lh + wh)

2

Substitute

Compute each face pair, then double the sum. 2(3·8+3·3+8·3) = 114

EX 2medium

Surface area of a 3×2×4 box?

1

Surface area of a box

Add the areas of all six faces — they come in three matching pairs. 2(lw + lh + wh)

2

Substitute

Compute each face pair, then double the sum. 2(3·2+3·4+2·4) = 52

EX 3hard

Surface area of a 3×2×3 box?

1

Surface area of a box

Add the areas of all six faces — they come in three matching pairs. 2(lw + lh + wh)

2

Substitute

Compute each face pair, then double the sum. 2(3·2+3·3+2·3) = 42

04 / COMMON TRAPS

Where students slip.

Trap

Computing volume instead.

Fix

Surface area adds faces; volume multiplies dimensions.

Trap

Counting only three faces.

Fix

There are six — three matching pairs.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Surface area of a 7×3×4 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
C2

Surface area of a 7×8×5 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
C3

Surface area of a 7×7×4 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
C4

Surface area of a 6×6×5 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
Apply

Apply (4)

A1

Surface area of a 6×4×8 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
A2

Surface area of a 4×7×3 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
A3

Surface area of a 3×2×3 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
A4

Surface area of a 8×4×3 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
Extension

Extension (4)

E1

Surface area of a 2×5×6 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
E2

Surface area of a 8×3×4 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
E3

Surface area of a 3×6×7 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.
E4

Surface area of a 7×2×7 box?

Need a hint?
  • Find the three face areas: lw, lh, wh.
  • Add them and double.