Perimeter and Area of 2D Shapes
Perimeter measures the distance around a shape. Area measures the surface inside it. Learn the difference, use formulas for squares, rectangles and triangles, and choose the correct units for each answer.
Learning time: approximately 30 minutes · Beginner level
What You Will Learn
- Explain the difference between perimeter and area.
- Calculate the perimeter of squares and rectangles.
- Calculate the area of squares and rectangles.
- Find the area of a triangle.
- Use correct units and solve practical problems.
1. Perimeter and Area: What Is the Difference?
Perimeter is the total distance around the outside edge of a 2D shape. Area is the amount of flat surface covered inside the shape.
Imagine putting a fence around a garden (perimeter) and covering the ground with grass (area).
Perimeter is measured in ordinary units such as centimetres (cm) or metres (m). Area is measured in square units such as cm² or m².
2. Perimeter of a Rectangle
A rectangle has two pairs of equal opposite sides. Add all four sides to find its perimeter.
Worked example
A rectangle is 8 cm long and 3 cm wide.
P = 2 × (8 + 3) = 2 × 11 = 22 cm.
3. Perimeter of a Square
A square has four equal sides. Multiply the length of one side by 4.
Worked example
A square has sides of 5 cm.
P = 4 × 5 = 20 cm.
4. Area of a Rectangle
Multiply the length by the width to find the area of a rectangle.
Worked example
A rectangle is 8 cm long and 3 cm wide.
A = 8 × 3 = 24 cm².
The square unit tells us that the area covers 24 squares, each measuring 1 cm by 1 cm.
5. Area of a Square
Because all sides of a square are equal, multiply the side length by itself.
Worked example
A square has a side length of 6 m.
A = 6 × 6 = 36 m².
6. Area of a Triangle
A triangle has half the area of a rectangle or parallelogram with the same base and perpendicular height.
Worked example
A triangle has a base of 10 cm and a perpendicular height of 4 cm.
A = 1/2 × 10 × 4 = 5 × 4 = 20 cm².
7. Choose the Correct Formula
| Shape | Perimeter | Area |
|---|---|---|
| Square (side s) | 4s | s × s |
| Rectangle (length l, width w) | 2(l + w) | l × w |
| Triangle (sides a, b, c) | a + b + c | 1/2 × base × perpendicular height |
8. Solve Everyday Problems
Example 1: Fencing a garden
A rectangular garden is 12 m long and 7 m wide. How much fencing is needed to go all the way around it?
P = 2 × (12 + 7) = 38. 38 metres of fencing are needed.
Example 2: Covering a floor
A rectangular room is 5 m long and 4 m wide. What is its floor area?
A = 5 × 4 = 20 m².
Example 3: A triangular sign
A triangular sign has a base of 8 cm and a perpendicular height of 6 cm. Find its area.
A = 1/2 × 8 × 6 = 24 cm².
9. Common Mistakes to Avoid
10. Practice Exercises
Try these before revealing the answers.
- Find the perimeter of a square with side 7 cm.
- Find the area of a square with side 7 cm.
- Find the perimeter of a rectangle 9 cm long and 4 cm wide.
- Find the area of a rectangle 9 cm long and 4 cm wide.
- Find the area of a triangle with base 12 cm and perpendicular height 5 cm.
- A rectangular field is 15 m long and 8 m wide. How much fencing is needed to go around it?
- What is the difference between 18 cm and 18 cm²?
Show practice answers and explanations
- 4 × 7 = 28 cm.
- 7 × 7 = 49 cm².
- 2 × (9 + 4) = 26 cm.
- 9 × 4 = 36 cm².
- 1/2 × 12 × 5 = 30 cm².
- 2 × (15 + 8) = 46 m of fencing.
- 18 cm is a length; 18 cm² is an area.
11. Test Your Understanding
Choose one answer for each question, then select Check Answers. Each question is worth one point.
12. Free Printable Worksheet
Print this worksheet or save it as a PDF for extra practice.
Learnora — Grade 6 Mathematics
Perimeter and Area Worksheet
Name: __________________________ Date: _______________
Instructions: Write the formula and show your working. Include the correct units.
- Find the perimeter of a square with side 9 cm.
- Find the area of a square with side 9 cm.
- Find the perimeter of a rectangle 11 m long and 6 m wide.
- Find the area of a rectangle 11 m long and 6 m wide.
- Find the area of a triangle with base 14 cm and perpendicular height 3 cm.
- A rectangular patio is 7 m long and 5 m wide. Find its area.
- A rectangular garden is 10 m by 4 m. Find the total length of fencing needed.
Keep practising — you are making progress!
Learnora — Learn Better. Practice Smarter.
Teacher / Parent Answer Key
- 4 × 9 = 36 cm.
- 9 × 9 = 81 cm².
- 2 × (11 + 6) = 34 m.
- 11 × 6 = 66 m².
- 1/2 × 14 × 3 = 21 cm².
- 7 × 5 = 35 m².
- 2 × (10 + 4) = 28 m.
13. Lesson Summary
- Perimeter is the distance around a 2D shape.
- Area is the surface covered inside a 2D shape.
- Rectangle perimeter = 2 × (length + width).
- Rectangle area = length × width.
- Square perimeter = 4 × side; square area = side × side.
- Triangle area = 1/2 × base × perpendicular height.
- Use ordinary units for perimeter and square units for area.
Educational note: This is a curriculum-neutral Grade 6 lesson. Teachers and parents can adapt examples and practice to their local curriculum.