P3 Area and Perimeter: Inside and Around

Imagine putting tiles on a classroom floor, then walking around its edge. The tiles cover the inside. Your walk traces the boundary. Those are two different measurements: area and perimeter.

Parents: let your child point to an inside square and an outside edge before calculating. Ask them to predict whether a change affects the area, the perimeter, or both.

By the end you will be able to count square units, use cm² and m² correctly, and find rectangle, square and rectilinear perimeters and areas.

Area fills the inside

Area tells how much surface is covered. On a unit grid, count the little squares inside. A 5-column by 3-row rectangle has 5 × 3 = 15 square units.

Perimeter walks around the boundary

Perimeter is the boundary distance. On the same 5 × 3 grid, walk 5 + 3 + 5 + 3 = 16 units around the outside. The 15 interior squares and the 16 boundary steps answer different questions.

Square units, cm² and m²

A little square with side 1 cm has area 1 cm². A little square with side 1 m has area 1 m². The number tells how many squares; the superscript ² tells you that the unit measures an area. P3 keeps cm² and m² as separate unit choices. Do not convert between them in this lesson.

Rectangle and square rules

For a rectangle, area is length × width and perimeter is the two lengths plus the two widths. For a square, all four sides match, so perimeter is 4 × side and area is side × side.

Rectangle and square

$$8\times3=24\,\text{ cm}^2$$

$$2\times(8+3)=22\,\text{ cm}$$

$$5\times5=25\,\text{ cm}^2$$

$$4\times5=20\,\text{ cm}$$

🔬

Area and perimeter grid lab

🤔 Predict first: A 5 by 3 grid has how many square units inside?

81516

The lab starts with the 5 × 3 grid, then changes the construction. The L-shaped case is intentionally a perimeter-only P3 walk: trace its six labelled sides, 6 + 2 + 2 + 3 + 4 + 5 = 22 cm. Do not split it into smaller rectangles to find an area here.

Three inside-and-around practice checks

Read every dimension and unit before opening a solution.

Practice 1 — a unit grid

A rectangle has 5 columns and 3 rows of unit squares. Find its area and perimeter in grid units.

Show the worked count

Count inside and around

$$5\times3=15\,\text{ square units}$$

$$5+3+5+3=16\,\text{ units}$$

The area is 15 square units and the perimeter is 16 units.

Practice 2 — a rectangle and a square

A rectangle is 8 cm long and 3 cm wide. A square has side 5 cm. Find the area of each and the perimeter of each.

Show the formulas and answers

Use the matching rule

$$8\times3=24\,\text{ cm}^2$$

$$2\times(8+3)=22\,\text{ cm}$$

$$5\times5=25\,\text{ cm}^2$$

$$4\times5=20\,\text{ cm}$$

The rectangle has area 24 cm² and perimeter 22 cm. The square has area 25 cm² and perimeter 20 cm.

Practice 3 — an L-shaped boundary

An L-shaped rectilinear outline has side lengths 6 cm, 2 cm, 2 cm, 3 cm, 4 cm and 5 cm. Find its perimeter. What area should you find in this P3 check?

Show the boundary-only solution

Trace every outside side

$$6+2+2+3+4+5=22\,\text{ cm}$$

$$\text{P3 check: perimeter only}$$

The perimeter is 22 cm. This check asks for no composite area.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 8 — your progress is saved on this device.

1. What does area measure?

   The surface covered insideThe walk around the edgeThe number of corners only

2. What does perimeter measure?

   The inside squaresThe distance around the boundaryThe width only

3. A 5 by 3 grid is made from unit squares. What is its area?

   15 square units16 square units8 square units

4. What is the perimeter of the same 5 by 3 grid?

   15 units16 units30 units

5. A rectangle is 8 cm by 3 cm. What is its area?

   22 cm²24 cm²24 cm

6. A square has side 5 cm. What is its perimeter?

   20 cm25 cm10 cm

7. What is the perimeter of the L-shape with sides 6, 2, 2, 3, 4 and 5 cm?

   20 cm22 cm24 cm

8. A 2 by 3 grid has 1 m² in each cell. Which answer uses the right area unit?

   6 m²6 m5 m²

See my score