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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.