Year 7 Maths: Perimeter

What is Perimeter?

Perimeter is the total distance around the outside of a shape. Imagine walking around a park or a garden; the path you take is the perimeter.

Key Points:

1. Definition: Perimeter is the sum of all the lengths of the sides of a shape.
2. Units: We measure perimeter in units like metres (m), centimetres (cm), or inches (in).
3. Shapes: The perimeter can be calculated for different shapes like squares, rectangles, triangles, and circles.

How to Calculate Perimeter

For Different Shapes

1. Rectangle

• Formula: $$P = 2 \times (length + width)$$
• Example: If a rectangle has a length of 5 cm and a width of 3 cm:
  • $$P = 2 \times (5 + 3) = 2 \times 8 = 16 , cm$$

2. Square

• Formula: $$P = 4 \times side$$
• Example: If a square has a side length of 4 cm:
  • $$P = 4 \times 4 = 16 , cm$$

3. Triangle

• Formula: $$P = side_1 + side_2 + side_3$$
• Example: If a triangle has sides of 3 cm, 4 cm, and 5 cm:
  • $$P = 3 + 4 + 5 = 12 , cm$$

4. Circle (Circumference)

• Formula: $$C = 2 \times \pi \times radius$$ (where $$\pi$$ is approximately 3.14)
• Example: If a circle has a radius of 2 cm:
  • $$C = 2 \times 3.14 \times 2 \approx 12.56 , cm$$

Tips and Tricks for Calculating Perimeter

1. Draw the Shape: If you’re unsure about the sides, sketch the shape first.
2. Use a Calculator: For complicated calculations, a calculator can help.
3. Check Your Units: Make sure all lengths are in the same unit before adding them together.

Questions on Perimeter

Easy Level Questions

1. What is the perimeter of a rectangle with a length of 6 cm and a width of 4 cm?
2. Calculate the perimeter of a square with each side measuring 5 cm.
3. If a triangle has sides measuring 2 cm, 3 cm, and 4 cm, what is its perimeter?
4. Find the perimeter of a rectangle with a length of 10 cm and a width of 2 cm.
5. What is the perimeter of a square with a side length of 8 cm?
6. A triangle has sides of 5 cm, 5 cm, and 5 cm. What is its perimeter?
7. Calculate the perimeter of a rectangle with a length of 7 cm and a width of 3 cm.
8. If you have a square with a side of 6 cm, what is its perimeter?
9. What is the perimeter of a triangle with sides of 1 cm, 2 cm, and 3 cm?
10. Find the perimeter of a rectangle with a length of 12 cm and a width of 5 cm.
11. A square has a perimeter of 40 cm. What is the length of one side?
12. If a rectangle has a length of 8 cm and a width of 4 cm, what is its perimeter?
13. Calculate the perimeter of a triangle with sides of 6 cm, 8 cm, and 10 cm.
14. What is the perimeter of a square that measures 3 cm on each side?
15. A rectangle has a perimeter of 30 cm. If the length is 10 cm, what is the width?
16. What is the perimeter of a triangle with sides of 7 cm, 1 cm, and 4 cm?
17. Calculate the perimeter of a square with a side length of 9 cm.
18. If the length of a rectangle is 5 cm and the width is 5 cm, what is the perimeter?
19. A triangle has a perimeter of 18 cm. If one side is 6 cm and another is 7 cm, what is the length of the third side?
20. What is the perimeter of a rectangle with a length of 14 cm and a width of 3 cm?

Medium Level Questions

1. Calculate the perimeter of a rectangle where the length is 15 cm and the width is 10 cm.
2. A square has a side length of 12 cm. What is its perimeter?
3. If a triangle has sides of 9 cm, 12 cm, and 15 cm, what is its perimeter?
4. Find the perimeter of a rectangle with a length of 20 cm and a width of 5 cm.
5. A regular hexagon has sides of 3 cm. What is its perimeter?
6. Calculate the perimeter of a rectangle with a length of 25 cm and a width of 10 cm.
7. If a square has a perimeter of 48 cm, what is the length of each side?
8. What is the perimeter of a triangle with sides measuring 7 cm, 8 cm, and 9 cm?
9. A rectangle has a perimeter of 50 cm. If the length is 20 cm, what is the width?
10. Find the perimeter of a square with a side length of 4 cm.
11. A triangle has sides measuring 5 cm, 6 cm, and 11 cm. What is its perimeter?
12. Calculate the perimeter of a rectangle with a length of 1 m and a width of 50 cm.
13. What is the perimeter of a triangle with sides measuring 10 cm, 10 cm, and 5 cm?
14. If a rectangle has a perimeter of 40 cm and a length of 15 cm, what is its width?
15. A square has a perimeter of 36 cm. What is the area of the square?
16. What is the perimeter of a triangle with sides of 2 cm, 5 cm, and 8 cm?
17. Calculate the perimeter of a rectangle with length 18 cm and width 7 cm.
18. Find the perimeter of a square that measures 10 cm on each side.
19. A triangle has a perimeter of 30 cm. If one side is 10 cm and another is 12 cm, what is the length of the third side?
20. What is the perimeter of a rectangle with a length of 30 cm and a width of 10 cm?

Hard Level Questions

1. A rectangular garden has a length of 14 m and a width of 9 m. What is its perimeter?
2. A regular octagon has a side length of 4 cm. What is its perimeter?
3. If a triangle has sides of 13 cm, 14 cm, and 15 cm, what is its perimeter?
4. A rectangle has a perimeter of 60 cm. If the width is 10 cm, what is the length?
5. Calculate the perimeter of a trapezium with bases of 8 cm and 5 cm and non-parallel sides of 4 cm and 6 cm.
6. A square has a side length of 16 cm. What is its perimeter?
7. Find the perimeter of a rectangle with a length of 12 m and a width of 4 m.
8. If a triangle has a perimeter of 24 cm and two sides are 8 cm and 9 cm, what is the length of the third side?
9. A circle has a radius of 10 cm. What is its circumference?
10. Calculate the perimeter of a rectangle with a length of 25 cm and a width of 15 cm.
11. A regular pentagon has a side length of 6 cm. What is its perimeter?
12. If a rectangle has a perimeter of 100 m and the length is 35 m, what is the width?
13. Find the perimeter of a triangle with sides measuring 5 m, 12 m, and 13 m.
14. A square has a perimeter of 64 cm. What is the area of the square?
15. Calculate the perimeter of a rectangle with a length of 40 cm and a width of 20 cm.
16. If a triangle has a perimeter of 30 cm and two sides are 12 cm and 10 cm, what is the length of the third side?
17. A circle has a diameter of 20 cm. What is its circumference?
18. Find the perimeter of a rectangle with length 50 cm and width 25 cm.
19. A triangle has a perimeter of 36 cm. If two sides measure 10 cm and 12 cm, what is the length of the third side?
20. What is the perimeter of a hexagon with a side length of 3 cm?

Answers and Explanations

Easy Level Answers

1. 20 cm
   • $$P = 2 \times (6 + 4) = 20$$
2. 20 cm
   • $$P = 4 \times 5 = 20$$
3. 9 cm
   • $$P = 2 + 3 + 4 = 9$$
4. 26 cm
   • $$P = 2 \times (10 + 2) = 26$$
5. 32 cm
   • $$P = 4 \times 8 = 32$$
6. 15 cm
   • $$P = 5 + 5 + 5 = 15$$
7. 20 cm
   • $$P = 7 + 3 + 7 + 3 = 20$$
8. 24 cm
   • $$P = 4 \times 6 = 24$$
9. 6 cm
   • $$P = 1 + 2 + 3 = 6$$
10. 34 cm
    • $$P = 12 + 5 + 12 + 5 = 34$$
11. 10 cm
    • $$P = 40 \div 4 = 10$$
12. 24 cm
    • $$P = 8 + 4 + 8 + 4 = 24$$
13. 24 cm
    • $$P = 6 + 8 + 10 = 24$$
14. 12 cm
    • $$P = 3 \times 4 = 12$$
15. 10 cm
    • $$P = 30 \div 3 = 10$$
16. 12 cm
    • $$P = 5 + 5 + 2 = 12$$
17. 36 cm
    • $$P = 4 \times 9 = 36$$
18. 20 cm
    • $$P = 5 + 5 + 5 + 5 = 20$$
19. 12 cm
    • $$P = 10 + 12 + 12 = 12$$
20. 34 cm
    • $$P = 30 + 10 + 10 = 34$$

Medium Level Answers

1. 50 cm
   • $$P = 2 \times (15 + 10) = 50$$
2. 48 cm
   • $$P = 4 \times 12 = 48$$
3. 36 cm
   • $$P = 9 + 12 + 15 = 36$$
4. 50 cm
   • $$P = 2 \times (20 + 5) = 50$$
5. 24 cm
   • $$P = 6 \times 4 = 24$$
6. 70 cm
   • $$P = 2 \times (25 + 10) = 70$$
7. 12 cm
   • $$P = 48 \div 4 = 12$$
8. 24 cm
   • $$P = 7 + 8 + 9 = 24$$
9. 5 cm
   • $$P = (50 – 20) \div 2 = 15$$
10. 16 cm
    • $$P = 4 \times 4 = 16$$
11. 26 cm
    • $$P = 5 + 6 + 11 = 26$$
12. 2 m
    • $$P = 1 + 0.5 + 1 + 0.5 = 2$$
13. 30 cm
    • $$P = 10 + 10 + 10 = 30$$
14. 24 cm
    • $$P = 40 \div 3 = 24$$
15. 25 cm
    • $$P = 100 – 70 = 25$$
16. 15 cm
    • $$P = 2 + 5 + 8 = 15$$
17. 62.83 cm
    • $$P = 2 \times 3.14 \times 10 \approx 62.83$$
18. 90 cm
    • $$P = 2 \times (25 + 20) = 90$$
19. 8 cm
    • $$P = 30 – 10 – 12 = 8$$
20. 80 cm
    • $$P = 2 \times (30 + 10) = 80$$

Hard Level Answers

1. 46 m
   • $$P = 2 \times (14 + 9) = 46$$
2. 32 cm
   • $$P = 8 \times 4 = 32$$
3. 42 cm
   • $$P = 13 + 14 + 15 = 42$$
4. 20 cm
   • $$P = (60 – 20) \div 2 = 20$$
5. 23 cm
   • $$P = 8 + 5 + 4 + 6 = 23$$
6. 64 cm
   • $$P = 4 \times 16 = 64$$
7. 32 m
   • $$P = 2 \times (12 + 4) = 32$$
8. 4 cm
   • $$P = 24 – 8 – 9 = 4$$
9. 62.83 cm
   • $$P = 2 \times 3.14 \times 10 \approx 62.83$$
10. 90 cm
    • $$P = 2 \times (25 + 15) = 90$$
11. 30 cm
    • $$P = 5 \times 6 = 30$$
12. 25 m
    • $$P = (100 – 70) \div 2 = 25$$
13. 30 m
    • $$P = 5 + 12 + 13 = 30$$
14. 256 cm²
    • $$A = 16 \times 16 = 256$$
15. 120 cm
    • $$P = 2 \times (40 + 20) = 120$$
16. 8 cm
    • $$P = 30 – 10 – 12 = 8$$
17. 62.83 cm
    • $$P = 2 \times 3.14 \times 10 \approx 62.83$$
18. 150 cm
    • $$P = 2 \times (50 + 25) = 150$$
19. 14 cm
    • $$P = 36 – 10 – 12 = 14$$
20. 18 cm
    • $$P = 6 \times 3 = 18$$

Feel free to ask any questions or for clarification on any topic! Remember, practice makes perfect!