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Door 12 · Grade 4

📏 Area and Perimeter Formulas

Perimeter measures the distance AROUND the boundary of a shape

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Perimeter of Rectangle and Square

Perimeter is the total distance around the outside of a shape — like walking around the boundary of a park.
Rectangle:
Perimeter = 2 x (Length + Width)
P = 2 x (l + w)
Why? A rectangle has 2 equal lengths and 2 equal widths.
Square:
All four sides are equal.
Perimeter = 4 x side (P = 4s)
To find a missing side: rearrange the formula. E.g. if P = 36 and l = 10, then 36 = 2(10+w), so w = 8.

Worked example

Problem: A rectangular garden is 12 m long and 8 m wide. Find its perimeter.

  1. P = 2 x (l + w) = 2 x (12 + 8) = 2 x 20 = 40 m.

Answer: 40 m.

Area of Rectangle and Square

Area is the amount of space INSIDE a shape. Think of it as the number of 1x1 squares that can fit inside.
Rectangle:
Area = Length x Width (A = l x w)
Square:
Area = side x side (A = s x s = s²)
Units: perimeter uses cm/m, but area uses square units — cm² or m².
To find a missing side when area is given: divide. E.g. if A = 54, l = 9, then w = 54 / 9 = 6.

Worked example

Problem: A rectangular hall is 15 m long and 10 m wide. Find its area.

  1. A = l x w = 15 x 10 = 150 m².

Answer: 150 square metres.

Relationship Between Area and Perimeter

Area and perimeter are related but measure different things:
• Perimeter = distance around (units: cm, m)
• Area = space inside (square units: cm², m²)

Two shapes can have the same perimeter but different areas, or the same area but different perimeters!
This is an important insight: a square always has the largest area for a given perimeter compared to other rectangles.

Worked example

Problem: A square has a perimeter of 48 cm. Find its area.

  1. Step 1: Find side from perimeter.
  2. P = 4s.
  3. 48 = 4s. s = 12 cm.
  4. Step 2: Find area.
  5. A = s x s = 12 x 12 = 144 cm².

Answer: A = s x s = 12 x 12 = 144 cm².