Year 5 Maths: Perimeters of Rectangles and Squares

Understanding Perimeters

Hello, Year 5! Today, we are going to learn about perimeters. The perimeter is the distance around the outside of a shape. For rectangles and squares, we can find the perimeter by adding up the lengths of all the sides.

What is a Rectangle?

A rectangle has two long sides and two short sides. The opposite sides are always the same length.

What is a Square?

A square is a special type of rectangle. It has four equal sides. This means all the sides are the same length.

How to Calculate Perimeter

Perimeter of a Rectangle

To find the perimeter of a rectangle, we use the following formula:

• Length is one of the long sides.
• Width is one of the short sides.

Perimeter of a Square

To find the perimeter of a square, we use this formula:

• Side is the length of one side of the square.

Examples

Example 1: Rectangle

Imagine we have a rectangle with a length of 8 cm and a width of 5 cm.

1. Write the formula: $$P = 2 \times (length + width)$$
2. Substitute the values: $$P = 2 \times (8 + 5)$$
3. Calculate: $$P = 2 \times 13$$ $$P = 26 , cm$$

So, the perimeter of the rectangle is 26 cm.

Example 2: Square

Now, let’s find the perimeter of a square with a side length of 4 cm.

1. Write the formula: $$P = 4 \times side$$
2. Substitute the value: $$P = 4 \times 4$$
3. Calculate: $$P = 16 , cm$$

So, the perimeter of the square is 16 cm.

Key Rules and Tips

1. Remember the Formulas: Keep the formulas for rectangles and squares in mind.
2. Units Matter: Always include the units (cm, m, etc.) in your answers.
3. Double Check: After calculating, it’s good to double-check your work.
4. Visualize: Draw the shapes. It helps to see what you are measuring!
5. Practice: The more you practice, the easier it gets!

Questions

Easy Level Questions

1. What is the perimeter of a square with a side of 3 cm?
2. Calculate the perimeter of a rectangle with a length of 5 cm and a width of 2 cm.
3. Find the perimeter of a square with a side length of 6 cm.
4. What is the perimeter of a rectangle with a length of 10 cm and a width of 4 cm?
5. If a square has a side of 1 cm, what is its perimeter?
6. Calculate the perimeter of a rectangle with a length of 7 cm and a width of 3 cm.
7. What is the perimeter of a square with a side of 8 cm?
8. Find the perimeter of a rectangle with a length of 12 cm and a width of 5 cm.
9. If a square has a side of 2 cm, what is its perimeter?
10. Calculate the perimeter of a rectangle with a length of 9 cm and a width of 6 cm.
11. What is the perimeter of a square with a side of 5 cm?
12. Find the perimeter of a rectangle with a length of 4 cm and a width of 2 cm.
13. If a square has a side of 10 cm, what is its perimeter?
14. Calculate the perimeter of a rectangle with a length of 6 cm and a width of 1 cm.
15. What is the perimeter of a square with a side of 7 cm?
16. Find the perimeter of a rectangle with a length of 11 cm and a width of 3 cm.
17. If a square has a side of 4 cm, what is its perimeter?
18. Calculate the perimeter of a rectangle with a length of 8 cm and a width of 2 cm.
19. What is the perimeter of a square with a side of 3 cm?
20. Find the perimeter of a rectangle with a length of 5 cm and a width of 5 cm.

Medium Level Questions

1. A rectangle has a length of 15 cm and a width of 10 cm. What is its perimeter?
2. Calculate the perimeter of a square with a side length of 12 cm.
3. If a rectangle’s length is twice its width and the width is 5 cm, what is the perimeter?
4. Find the perimeter of a rectangle with a length of 20 cm and a width of 4 cm.
5. A square has a perimeter of 36 cm. What is the length of one side?
6. Calculate the perimeter of a rectangle with a length of 13 cm and a width of 7 cm.
7. If a square has a side length of 9 cm, what is its perimeter?
8. A rectangle has a perimeter of 50 cm. If the length is 18 cm, what is the width?
9. Calculate the perimeter of a square with a side length of 11 cm.
10. A rectangle has a length of 14 cm and a width of 5 cm. What is its perimeter?
11. If a square has a perimeter of 32 cm, what is the length of one side?
12. Find the perimeter of a rectangle with a length of 16 cm and a width of 8 cm.
13. A square has a side length that is 3 times longer than another square with a side length of 4 cm. What is the perimeter of the larger square?
14. Calculate the perimeter of a rectangle with a length of 25 cm and a width of 10 cm.
15. If a square has a side length of 5 cm and you double it, what is the new perimeter?
16. A rectangle has a length of 30 cm and a width of 10 cm. What is its perimeter?
17. Find the perimeter of a square with a side length of 15 cm.
18. A rectangle has a perimeter of 60 cm. If the width is 12 cm, what is the length?
19. Calculate the perimeter of a rectangle with a length of 22 cm and a width of 6 cm.
20. If a square has a perimeter of 44 cm, what is the length of one side?

Hard Level Questions

1. A rectangle’s length is 3 times its width. If the width is 4 cm, what is the perimeter?
2. Find the perimeter of a rectangle with a length of 30 cm and a width of 15 cm.
3. A square has a side length of x cm. If its perimeter is 48 cm, what is the value of x?
4. Calculate the perimeter of a rectangle with a length of 50 cm and a width of 20 cm.
5. If a square’s perimeter is 64 cm, what is the area of the square?
6. A rectangle has a length that is 6 cm more than its width. If the width is w cm, express the perimeter in terms of w.
7. Find the perimeter of a rectangle with a length of 18 cm and a width of 9 cm.
8. A square has a perimeter of 60 cm. If you cut each side in half, what is the new perimeter?
9. Calculate the perimeter of a rectangle with a length of 23 cm and a width of 17 cm.
10. If a rectangle’s perimeter is 100 cm and the length is twice the width, what are the dimensions?
11. A rectangle has a perimeter of 72 cm. If the length is 5 cm more than the width, what are the dimensions?
12. Find the perimeter of a square whose side length is 4 cm less than the side length of another square with a perimeter of 28 cm.
13. A rectangle has a length of 45 cm and a width of 30 cm. Calculate its perimeter.
14. If a square has a perimeter of 80 cm, what is the area of the square?
15. A rectangle has a width of 12 cm and a length that is 3 cm more than twice the width. What is the perimeter?
16. Calculate the perimeter of a rectangle with a length of 100 cm and a width of 40 cm.
17. A square’s perimeter is equal to the perimeter of a rectangle with length 24 cm and width 10 cm. What is the side length of the square?
18. If the perimeter of a square is equal to the perimeter of a rectangle with length 30 cm and width 10 cm, what is the length of one side of the square?
19. Find the perimeter of a rectangle whose length is 5 cm less than twice its width, and whose width is 8 cm.
20. A square has a perimeter of 96 cm. If each side is increased by 2 cm, what is the new perimeter?

Answers

Easy Level Answers

1. 12 cm
2. 14 cm
3. 24 cm
4. 28 cm
5. 4 cm
6. 20 cm
7. 32 cm
8. 34 cm
9. 8 cm
10. 30 cm
11. 20 cm
12. 12 cm
13. 40 cm
14. 20 cm
15. 28 cm
16. 18 cm
17. 16 cm
18. 20 cm
19. 12 cm
20. 30 cm

Medium Level Answers

1. 50 cm
2. 48 cm
3. 20 cm
4. 48 cm
5. 9 cm
6. 40 cm
7. 36 cm
8. 8 cm
9. 44 cm
10. 38 cm
11. 8 cm
12. 48 cm
13. 36 cm
14. 70 cm
15. 40 cm
16. 80 cm
17. 12 cm
18. 30 cm
19. 34 cm
20. 11 cm

Hard Level Answers

1. 28 cm
2. 90 cm
3. 12 cm
4. 140 cm
5. 64 cm
6. $$P = 2(w + w + 6) = 2(2w + 6) = 4w + 12$$
7. 54 cm
8. 60 cm
9. 80 cm
10. Length = 20 cm, Width = 10 cm
11. Length = 30 cm, Width = 15 cm
12. 8 cm
13. 150 cm
14. 400 cm²
15. 60 cm
16. 280 cm
17. 24 cm
18. 40 cm
19. 42 cm
20. 104 cm

Now, go ahead and practice these questions to become a pro at finding the perimeters of rectangles and squares! Happy learning!