Geometry · Surface area & volume · 4.4

Triangular prisms.

For ANY prism, volume = area of the base × length. A triangular prism has a triangle base (½bh), so volume = ½ × b × h × length. Base 6, height 4, length 10: ½ × 6 × 4 × 10 = 120.

01 / THE IDEA

See it work.

The figure

See the shape.

b=6h=4

Watch the method

Triangular prisms

Volume of a prism = base area × length.

1 / 2
1

Volume of a triangular prism

Area of the triangular base (½bh) times the length.

12bh×L\tfrac{1}{2}bh \times L
2

Substitute

Find the triangle area, then times the length.

12(6)(4)×10=120\tfrac{1}{2}(6)(4)\times 10 = 120
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.

Base area × length

Every prism is its base shape extended along a length.

Why it works

A wedge of cheese.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Volume of a triangular prism: base 10, height 5, length 12?

1

Volume of a triangular prism

Area of the triangular base (½bh) times the length. 1/2bh × L

2

Substitute

Find the triangle area, then times the length. 1/2(10)(5)× 12 = 300

EX 2medium

Volume of a triangular prism: base 6, height 6, length 7?

1

Volume of a triangular prism

Area of the triangular base (½bh) times the length. 1/2bh × L

2

Substitute

Find the triangle area, then times the length. 1/2(6)(6)× 7 = 126

EX 3hard

Volume of a triangular prism: base 7, height 7, length 8?

1

Volume of a triangular prism

Area of the triangular base (½bh) times the length. 1/2bh × L

2

Substitute

Find the triangle area, then times the length. 1/2(7)(7)× 8 = 196

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting the ½ for the triangle base.

Fix

The triangular base is ½ × b × h.

Trap

Multiplying only two dimensions.

Fix

It’s base area times the length.

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

Volume of a triangular prism: base 9, height 4, length 12?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
C2

Volume of a triangular prism: base 11, height 9, length 8?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
C3

Volume of a triangular prism: base 11, height 8, length 8?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
C4

Volume of a triangular prism: base 11, height 7, length 7?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
Apply

Apply (4)

A1

Volume of a triangular prism: base 12, height 8, length 6?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
A2

Volume of a triangular prism: base 6, height 4, length 9?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
A3

Volume of a triangular prism: base 12, height 4, length 11?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
A4

Volume of a triangular prism: base 8, height 9, length 11?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
Extension

Extension (4)

E1

Volume of a triangular prism: base 12, height 7, length 8?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
E2

Volume of a triangular prism: base 5, height 5, length 6?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
E3

Volume of a triangular prism: base 6, height 8, length 12?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.
E4

Volume of a triangular prism: base 5, height 6, length 5?

Need a hint?
  • Find the triangle base area ½bh.
  • Multiply by the length.