Geometry · Perimeter & area · 3.1

Peri- meter.

Perimeter is the total distance around a shape — just add all the side lengths. For a rectangle that’s 2(length + width). An 8 × 5 rectangle has perimeter 2(8 + 5) = 26.

01 / THE IDEA

See it work.

The figure

See the shape.

85

Watch the method

Perimeter

Perimeter of a rectangle = 2(l + w).

1 / 2
1

Perimeter of a rectangle

Add all four sides: two lengths and two widths.

2(l+w)2(l + w)
2

Substitute

Plug in the length and width.

2(8+5)=262(8 + 5) = 26
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.

Walk the boundary

Perimeter is the fence around the shape: the sum of its sides.

Why it works

Once around the edge.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Perimeter of a 5×10 rectangle?

1

Perimeter of a rectangle

Add all four sides: two lengths and two widths. 2(l + w)

2

Substitute

Plug in the length and width. 2(5 + 10) = 30

EX 2medium

Perimeter of a 13×7 rectangle?

1

Perimeter of a rectangle

Add all four sides: two lengths and two widths. 2(l + w)

2

Substitute

Plug in the length and width. 2(13 + 7) = 40

EX 3hard

Perimeter of a 8×13 rectangle?

1

Perimeter of a rectangle

Add all four sides: two lengths and two widths. 2(l + w)

2

Substitute

Plug in the length and width. 2(8 + 13) = 42

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying instead of adding.

Fix

Perimeter adds sides; area multiplies.

Trap

Counting only two sides.

Fix

A rectangle has two lengths AND two widths.

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

Perimeter of a 10×7 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
C2

Perimeter of a 12×5 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
C3

Perimeter of a 7×4 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
C4

Perimeter of a 4×14 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
Apply

Apply (4)

A1

Perimeter of a 11×10 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
A2

Perimeter of a 6×4 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
A3

Perimeter of a 4×11 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
A4

Perimeter of a 12×7 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
Extension

Extension (4)

E1

Perimeter of a 6×13 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
E2

Perimeter of a 10×6 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
E3

Perimeter of a 4×6 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).
E4

Perimeter of a 14×5 rectangle?

Need a hint?
  • Add all the sides.
  • Rectangle: 2(l + w).