Geometry · Perimeter & area · 3.3

Area of a triangle.

A triangle is exactly half of a rectangle with the same base and height, so its area is ½ × base × height. Base 10, height 4: ½ × 10 × 4 = 20. The height must be perpendicular to the base.

01 / THE IDEA

See it work.

The figure

See the shape.

b=10h=4

Watch the method

Area of a triangle

Area of a triangle = ½ × base × height.

1 / 2
1

Area of a triangle

A triangle is half of a rectangle: ½ base × height.

12bh\tfrac{1}{2} b h
2

Substitute

Half of base times height.

12×10×4=20\tfrac{1}{2}\times 10\times 4 = 20
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.

Half a rectangle

Two copies of a triangle make a rectangle, so one is half its area.

Why it works

Cut a rectangle along the diagonal.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Area of a triangle, base 14, height 4?

1

Area of a triangle

A triangle is half of a rectangle: ½ base × height. 1/2 b h

2

Substitute

Half of base times height. 1/2× 14× 4 = 28

EX 2medium

Area of a triangle, base 11, height 9?

1

Area of a triangle

A triangle is half of a rectangle: ½ base × height. 1/2 b h

2

Substitute

Half of base times height. 1/2× 11× 9 = 49.5

EX 3hard

Area of a triangle, base 14, height 3?

1

Area of a triangle

A triangle is half of a rectangle: ½ base × height. 1/2 b h

2

Substitute

Half of base times height. 1/2× 14× 3 = 21

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting the ½.

Fix

A triangle is HALF of base × height.

Trap

Using a slanted side as the height.

Fix

The height is perpendicular to the base.

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

Area of a triangle, base 16, height 11?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
C2

Area of a triangle, base 4, height 4?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
C3

Area of a triangle, base 13, height 5?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
C4

Area of a triangle, base 10, height 12?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
Apply

Apply (4)

A1

Area of a triangle, base 7, height 9?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
A2

Area of a triangle, base 12, height 4?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
A3

Area of a triangle, base 6, height 8?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
A4

Area of a triangle, base 4, height 10?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
Extension

Extension (4)

E1

Area of a triangle, base 13, height 8?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
E2

Area of a triangle, base 9, height 12?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
E3

Area of a triangle, base 10, height 11?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.
E4

Area of a triangle, base 16, height 9?

Need a hint?
  • Use ½ × base × height.
  • Height is perpendicular to the base.