Area and Perimeter Formulas • Topic 3 of 3

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.

Same Perimeter = 24 m, Different Areas!10m x 2mArea = 20 m2P = 24 m8m x 4mArea = 32 m2P = 24 m6m x 6mArea = 36 m2P = 24 mSquare has the LARGEST area for the same perimeter!
Solved Examples
1
Worked Example
A square has a perimeter of 48 cm. Find its area.
SolutionStep 1: Find side from perimeter. P = 4s. 48 = 4s. s = 12 cm. Step 2: Find area. A = s x s = 12 x 12 = 144 cm².
2
Worked Example
A square has an area of 64 m². Find its perimeter.
SolutionStep 1: Find side from area. A = s x s. 64 = s x s. s = 8 m (since 8 x 8 = 64). Step 2: Find perimeter. P = 4 x 8 = 32 m.
3
Worked Example
A farmer has a rectangular field 10 m x 25 m. Fencing costs Rs.15 per metre. Find the fencing cost and area of the field.
SolutionPerimeter = 2(10+25) = 2 x 35 = 70 m. Fencing cost = 70 x 15 = Rs.1,050. Area = 10 x 25 = 250 m².

Key Points

  • Same perimeter does NOT mean same area!
  • Square gives the largest area for a given perimeter
  • Perimeter units: cm, m (linear); Area units: cm2, m2 (square)
  • To find perimeter from area: first find the side, then use the formula
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.Two shapes can have the same perimeter but different:
Explanation: Same perimeter, different area.
Q2.Perimeter is a ___; area is a surface.
Explanation: Length.
Q3.Perimeter is measured in cm; area is measured in:
Explanation: cm$^2$.
Q4.For a fixed perimeter, the shape with the largest area is a:
Explanation: A square.
Practice more MCQs → 📝 Assignment · 35 marks