Geometry · Apply · 5.1

Flooring & paint.

Covering a surface — tiling a floor, painting a wall — is an area problem: multiply length × width to get the square units needed. A 12 × 9 room needs 108 square units of flooring.

01 / THE IDEA

See it work.

The figure

See the shape.

129

Watch the method

Flooring & paint

Surface to cover → area = l × w.

1 / 2
1

Area of a rectangle

Area is length times width.

l×wl \times w
2

Multiply

Multiply the two dimensions.

12×9=10812 \times 9 = 108
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.

Cover the surface

How much material to cover a flat region is its area.

Why it works

Tiles fill the floor.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Area of a 10×8 rectangle?

1

Area of a rectangle

Area is length times width. l × w

2

Multiply

Multiply the two dimensions. 10 × 8 = 80

EX 2medium

Area of a 5×14 rectangle?

1

Area of a rectangle

Area is length times width. l × w

2

Multiply

Multiply the two dimensions. 5 × 14 = 70

EX 3hard

Area of a 9×5 rectangle?

1

Area of a rectangle

Area is length times width. l × w

2

Multiply

Multiply the two dimensions. 9 × 5 = 45

04 / COMMON TRAPS

Where students slip.

Trap

Using perimeter for covering.

Fix

Covering a surface is area, not perimeter.

Trap

Wrong units.

Fix

Area comes out in square units.

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 13×6 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
C2

Area of a 7×4 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
C3

Area of a 11×5 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
C4

Area of a 12×5 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
Apply

Apply (4)

A1

Area of a 9×5 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
A2

Area of a 13×13 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
A3

Area of a 5×13 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
A4

Area of a 9×3 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
Extension

Extension (4)

E1

Area of a 5×5 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
E2

Area of a 4×3 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
E3

Area of a 9×5 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.
E4

Area of a 4×9 rectangle?

Need a hint?
  • Covering a surface → area.
  • Multiply length × width.