Functional Skills Level 2 — Shape: Perimeter and Area

Perimeter

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Learning Objectives

Real-World Applications

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What is Perimeter?

Perimeter is the total distance around the outside of a shape. You find it by adding up all the side lengths.

Perimeter = sum of all sides  |  Rectangle: P = 2(l + w)
Tip: Perimeter is a length — measured in cm, m, km etc. (not cm² or m²). Always include the unit in your answer.
8 cm 5 cm P = 2(8 + 5) = 26 cm

Example 1: A rectangle is 8.5 m long and 3.2 m wide. Find the perimeter.

Step 1
\(P = 2(l + w) = 2(8.5 + 3.2) = 2 \times 11.7 = \mathbf{23.4\text{ m}}\)
✓ Quick Check 1 — Perimeter of Rectangles and Squares
Question 1 of 10
Perimeter of a Triangle

For any triangle, add all three sides together.

7 cm 5 cm 6 cm P = 7 + 5 + 6 = 18 cm

Example 2: A triangle has sides 7 cm, 5 cm, and 6 cm. Find its perimeter.

Step 1
\(P = 7 + 5 + 6 = \mathbf{18\text{ cm}}\)
Compound Shapes (L-shapes)

For compound shapes, you must first find any missing side lengths before adding all sides together.

Watch out: Missing sides on compound shapes are found using subtraction — look at the opposite parallel sides.
6 cm 8 cm 10 cm 4 cm 4 cm (10−6=4) 4 cm (8−4=4) P = 6+8+10+4+4+4 = 36 cm

Example 3: Find the perimeter of the L-shape above.

Step 1
Find missing sides: horizontal gap = 10 − 6 = 4 cm; vertical step = 8 − 4 = 4 cm
Step 2
\(P = 6 + 8 + 10 + 4 + 4 + 4 = \mathbf{36\text{ cm}}\)

Example 4: A shape has perimeter 45 cm. Five sides are 7, 9, 8, 6, and 10 cm. Find the sixth side.

Step 1
Sum of known sides: \(7+9+8+6+10 = 40\)
Step 2
Sixth side: \(45 - 40 = \mathbf{5\text{ cm}}\)
✓ Quick Check 2 — Perimeter of Triangles and Polygons
Question 1 of 10
Area vs Perimeter — They Are Different!

Two shapes can have the same area but different perimeters. This is a common exam trap.

4 m 3 m Area = 12 m² P = 14 m 3 × 4 rectangle ≠ perimeters 6 m 2 m Area = 12 m² P = 16 m 2 × 6 rectangle Both have area = 12 m² but different perimeters!
Remember: Area is measured in square units (cm², m²). Perimeter is measured in linear units (cm, m). Never confuse them!
A circle's perimeter is called its circumference — you'll learn how to calculate it in Lesson 12.6 — Circumference of Circles.
✓ Quick Check 3 — Real Life and Missing Sides
Question 1 of 10

Practice: Extra Questions

Work out each answer, then type it in and click Check to see if you're right.

# Question Your answer Result
1 Rectangle: length = 5 cm, width = 3 cm. Perimeter = ?
2 Square: side = 7 cm. Perimeter = ?
3 Triangle with sides 5 cm, 7 cm and 9 cm. Perimeter = ?
4 Rectangle: length = 10 cm, width = 4 cm. Perimeter = ?
5 Regular pentagon with side = 6 cm. Perimeter = ?
6 Square: perimeter = 36 cm. What is the side length?
7 Equilateral triangle with side = 8 cm. Perimeter = ?
8 Square, side = 6 cm. Perimeter = ?
9 Rectangle: 9 cm × 3 cm. Perimeter = ?
10 Triangle: sides 3, 4, 5 cm. Perimeter = ?
11 Regular pentagon, side = 7 cm. Perimeter = ?
12 Rectangle: 12 m × 5 m. Perimeter = ?

⚠ Things to Watch Out For

  • Perimeter is the total distance around the outside — don't confuse it with area (the space inside).
  • For compound shapes, don't include internal lines — only add the sides that form the outer boundary.
  • Work out any missing side lengths before adding — use the given dimensions to calculate unknowns.
  • Perimeter is measured in units (cm, m, etc.), not square units — don't write cm².
  • For a semicircle, the perimeter includes the curved arc (½ × πd) plus the straight diameter — don't forget the straight edge.
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