Geometry · Perimeter & area · 3.4

Parallelograms & trapezoids.

A parallelogram’s area is base × height (perpendicular height, not the slant). A trapezoid averages its two parallel sides, then times the height: ½(b₁ + b₂) × h. Bases 6 and 10, height 4: ½(16) × 4 = 32.

01 / THE IDEA

See it work.

The figure

See the shape.

Watch the method

Parallelograms & trapezoids

Parallelogram: b × h. Trapezoid: ½(b₁ + b₂) × h.

1 / 2

Area of a trapezoid

Average the two parallel sides, then times the height.

\tfrac{1}{2}(b_1 + b_2)h

Substitute

Add the bases, halve, times height.

\tfrac{1}{2}(6+10)\times 4 = 32

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.

Average the bases

A trapezoid acts like a rectangle whose width is the average of its parallel sides.

Why it works

Halfway between the two bases.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Area of a trapezoid, bases 9 and 10, height 3?

Area of a trapezoid

Average the two parallel sides, then times the height. 1/2(b_1 + b_2)h

Substitute

Add the bases, halve, times height. 1/2(9+10)× 3 = 28.5

EX 2medium

Area of a trapezoid, bases 5 and 14, height 5?

Area of a trapezoid

Average the two parallel sides, then times the height. 1/2(b_1 + b_2)h

Substitute

Add the bases, halve, times height. 1/2(5+14)× 5 = 47.5

EX 3hard

Area of a trapezoid, bases 4 and 12, height 7?

Area of a trapezoid

Average the two parallel sides, then times the height. 1/2(b_1 + b_2)h

Substitute

Add the bases, halve, times height. 1/2(4+12)× 7 = 56

04 / COMMON TRAPS

Where students slip.

Trap

Using the slant side as height.

Fix

Height is the perpendicular distance.

Trap

Forgetting to average for a trapezoid.

Fix

Add the two bases and halve before × height.

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)

Area of a trapezoid, bases 7 and 14, height 3?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 7 and 14, height 5?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 8 and 16, height 7?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 9 and 14, height 9?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Apply

Apply (4)

Area of a trapezoid, bases 4 and 10, height 5?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 7 and 15, height 6?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 4 and 16, height 6?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 5 and 12, height 9?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Extension

Extension (4)

Area of a trapezoid, bases 8 and 15, height 4?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 6 and 11, height 7?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 4 and 11, height 9?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.

Area of a trapezoid, bases 4 and 14, height 8?

Need a hint?

Trapezoid: average the parallel sides.
Then multiply by the height.