Perimeter — Grade 4 Mathematics
In Grade 4, we calculate perimeters of all polygons, find missing sides when the perimeter is given, use algebraic expressions for sides, and solve real-world perimeter problems.
Key Perimeter Formulas
Square: P = 4s e.g., s=7 cm → P = 28 cm
Regular polygon (n sides, side s): P = n × s e.g., regular hexagon, s=4 cm → P = 6 × 4 = 24 cm
Any polygon: P = sum of all sides
P = 2(8+5) = 26 cm
P = 4 × 6 = 24 cm
Finding Missing Sides
For a rectangle: if P = 34 cm and l = 10 cm → w = P/2 − l = 17 − 10 = 7 cm.
Worked Examples
A regular hexagon has a perimeter of 54 cm. Find the length of one side.
- A regular hexagon has 6 equal sides.
- One side = 54 ÷ 6 = 9 cm
A rectangle has perimeter 48 cm and length 15 cm. Find the width.
- P = 2(l + w) → 48 = 2(15 + w)
- 24 = 15 + w
- w = 24 − 15 = 9 cm
A rectangular garden is 12.5 m long and 7.8 m wide. Fencing costs £4 per metre. What is the total cost?
- P = 2(12.5 + 7.8) = 2 × 20.3 = 40.6 m
- Cost = 40.6 × 4 = £162.40
Practice Questions
1. Find the perimeter of a rectangle with length 14 cm and width 9 cm.
2. A square has perimeter 68 cm. Find the side length.
3. A rectangle has perimeter 52 cm and width 8 cm. Find the length.
4. A regular pentagon has perimeter 60 cm. Find one side length.
5. An irregular triangle has sides 8.5 cm, 11.2 cm, and 9.8 cm. What is its perimeter?
Key Points to Remember
- Perimeter = total distance around the outside of a shape.
- Rectangle: P = 2(l + w); Square: P = 4s.
- Regular polygon: P = number of sides × side length.
- To find a missing side: P − (sum of known sides) = missing side.
- Always include units (cm, m) in your answer.