📏 Perimeter and Area

KS3 Mathematics Worksheet

🎓 Mini-Lesson: Perimeter and Area of Shapes

What's the Difference?

Perimeter is the distance around the outside of a shape (measured in cm, m, etc.)

Area is the space inside a shape (measured in cm², m², etc.)

Rectangle
length (l)
width (w)
Perimeter = 2 × length + 2 × width
or: P = 2l + 2w or P = 2(l + w)
Area = length × width
or: A = l × w
Example: Rectangle with length 8cm and width 5cm
  • Perimeter: 2(8 + 5) = 2 × 13 = 26 cm
  • Area: 8 × 5 = 40 cm²
    • Square
    Perimeter = 4 × side
    or: P = 4s
    Area = side × side
    or: A = s²
    Example: Square with side 6cm
  • Perimeter: 4 × 6 = 24 cm
  • Area: 6² = 6 × 6 = 36 cm²
    • Triangle
    Perimeter = side₁ + side₂ + side₃
    (add all three sides)
    Area = ½ × base × height
    or: A = ½bh
    Example: Triangle with base 10cm, height 6cm, and other sides 8cm and 8cm
  • Perimeter: 10 + 8 + 8 = 26 cm
  • Area: ½ × 10 × 6 = 5 × 6 = 30 cm²
    • Circle
    Circumference (perimeter of a circle) = 2 × π × radius
    or: C = 2πr or C = πd (where d = diameter)
    Area = π × radius²
    or: A = πr²
    Remember: π (pi) ≈ 3.14 or 3.142
    Use the π button on your calculator for more accuracy!
    Example: Circle with radius 5cm (using π = 3.14)
  • Circumference: 2 × 3.14 × 5 = 31.4 cm
  • Area: 3.14 × 5² = 3.14 × 25 = 78.5 cm²
    • 💡 Top Tips:
    • Perimeter uses single units (cm, m)
    • Area uses squared units (cm², m²)
    • For triangles, make sure you use the HEIGHT (perpendicular to base), not a slanted side
    • Always include units in your answer!

    ✏️ Practice Questions

    Calculate the perimeter or area as requested. Include units!