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Geometry › Area & perimeter

Area & perimeter

Perimeter is the distance around the edge. Area is the surface inside. Different things, often confused.

Rectangle workshop

Drag the corner — watch area and perimeter change

w = 180h = 120
stage 360×360

Area

21600sq units

Perimeter

600units

Aspect

1.50w : h

Area = w × h = 180 × 120

Perimeter = 2(w + h) = 2 × (180 + 120)

Perimeter

Perimeter is the total length of all the sides. Imagine an ant walking around the outside of a shape — the perimeter is how far it walks.

  • Rectangle: P = 2(w + h)
  • Square: P = 4s
  • Triangle: add the three sides.
  • Circle: P = 2πr (called circumference).

Area

Area is how much surface a shape covers — measured in square units. A 3×4 rectangle has an area of 12 because you can fit 12 unit squares inside.

  • Rectangle: A = w × h
  • Square: A = s²
  • Triangle: A = ½ × base × height
  • Circle: A = π r²
  • Parallelogram: A = base × height
  • Trapezium: A = ½(a + b) × h

Same perimeter ≠ same area

A 1×9 rectangle and a 3×3 square both have a perimeter of 20. But the rectangle's area is 9 and the square's is 9 too — wait, try 2×8. That has perimeter 20 but area 16. The square gives the biggest area for any given rectangular perimeter.

Units

Perimeter is in units (cm, m, in). Area is in square units (cm², m², in²). Mixing them up is one of the most common mistakes on a test — always check.