Perimeter — Grade 5 Mathematics
In Grade 5, we calculate the perimeter of shapes where some sides are expressed algebraically, find missing sides using known perimeters, and are introduced to the circumference of a circle.
Perimeter Formulae Recap
Algebraic Perimeters
A rectangle has length (2x + 3) cm and width (x + 1) cm. Write an expression for the perimeter.
- P = 2[(2x + 3) + (x + 1)] = 2[3x + 4] = 6x + 8 cm
- If x = 5: P = 6(5) + 8 = 38 cm
Circumference of a Circle
The circumference is the distance around a circle. The diameter (d) is the distance straight across through the centre; the radius (r) is half the diameter.
Worked Examples
An isosceles triangle has two equal sides of length (3a) cm and a base of 8 cm. The perimeter is 32 cm. Find a.
- P = 3a + 3a + 8 = 6a + 8
- 6a + 8 = 32 → 6a = 24 → a = 4
- Each equal side = 3(4) = 12 cm
Find the circumference of a circle with diameter 7 cm (π ≈ 3.14).
- C = π × d = 3.14 × 7 = 21.98 cm
A circle has circumference 62.8 cm. Find its diameter and radius.
- C = π × d → 62.8 = 3.14 × d
- d = 62.8 ÷ 3.14 = 20 cm
- r = 20 ÷ 2 = 10 cm
Practice Questions
1. A rectangle has length (x + 4) cm and width x cm. The perimeter is 36 cm. Find x.
2. Find the circumference of a circle with diameter 15 cm (use π ≈ 3.14).
3. Find the circumference of a circle with radius 9 cm (use π ≈ 3.14).
4. A regular hexagon has perimeter 54 cm. What is the length of each side?
5. A square has side length (2n − 1) cm. If the perimeter is 44 cm, find n.
Key Points to Remember
- Perimeter is the total distance around a shape — add all the sides.
- Rectangle: P = 2(l + w); regular polygon: P = n × s.
- For algebraic sides, write an expression, simplify, then use the known perimeter to find the variable.
- Circumference of a circle: C = π × d (use π ≈ 3.14).
- Diameter = 2 × radius; to find diameter from circumference, divide by π.