Year 5 Maths: Perimeters of Composite Shapes

Introduction to Composite Shapes

Hello Year 5! Today, we are going to learn about the perimeters of composite shapes. A composite shape is made up of two or more simple shapes, like rectangles, squares, triangles, or circles.

What is Perimeter?

First, let’s remember what perimeter means. The perimeter is the total distance around a shape. To find the perimeter, we need to add up the lengths of all the sides.

How to Find the Perimeter of Composite Shapes

When we have a composite shape, we can break it down into its simple shapes. Here’s how we can do it:

1. Identify the Simple Shapes: Look at the composite shape and see what simple shapes it is made of.
2. Measure the Sides: If the side lengths are given, write them down. If not, you may need to measure them.
3. Calculate the Perimeter of Each Simple Shape: Use the formula for each shape:
   • For a rectangle: $$\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$$
   • For a square: $$\text{Perimeter} = 4 \times \text{Side}$$
   • For a triangle: $$\text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3}$$
4. Add the Perimeters Together: Finally, add the perimeters of all the simple shapes to get the total perimeter of the composite shape.

Example

Let’s look at an example:

Imagine you have a shape that is made of a rectangle and a square.

• Rectangle: Length = 5 cm, Width = 3 cm
• Square: Side = 4 cm

Step 1: Calculate the perimeter of the rectangle:

Step 2: Calculate the perimeter of the square:

Step 3: Add the two perimeters together:

So, the perimeter of the composite shape is 32 cm.

Key Rules & Tips

• Always write down the measurements of each side.
• Double-check your calculations to make sure you added correctly.
• If the shape is tricky, draw it out and label each part.
• Remember that sometimes you can find missing lengths if you know the total length of a side.

Questions for You

Now it’s your turn to practice! Here are some questions to help you understand better.

Easy Level Questions (20 questions)

1. What is the perimeter of a square with each side measuring 2 cm?
2. Calculate the perimeter of a rectangle with a length of 4 cm and a width of 3 cm.
3. A triangle has sides measuring 3 cm, 4 cm, and 5 cm. What is its perimeter?
4. Find the perimeter of a rectangle with a length of 6 cm and a width of 2 cm.
5. If a square has a perimeter of 20 cm, what is the length of one side?
6. What is the perimeter of a composite shape made of two squares, each side measuring 1 cm?
7. How many cm is the perimeter of a rectangle with a length of 5 cm and a width of 5 cm?
8. A triangle has sides of 2 cm, 3 cm, and 6 cm. Find its perimeter.
9. What is the perimeter of a square with each side measuring 10 cm?
10. Find the perimeter of a rectangle with a length of 8 cm and a width of 3 cm.
11. A composite shape has a rectangle (length 4 cm, width 2 cm) and a square (side 2 cm). What is the perimeter?
12. Calculate the perimeter of a triangle with sides measuring 5 cm, 5 cm, and 6 cm.
13. What is the perimeter of a square with sides measuring 15 cm?
14. Find the perimeter of a rectangle that is 7 cm long and 4 cm wide.
15. If one side of a square measures 3 cm, what is the total perimeter?
16. A composite shape consists of a rectangle (length 3 cm, width 2 cm) and a square (side 3 cm). What is the perimeter?
17. What is the perimeter of a triangle with sides measuring 7 cm, 8 cm, and 9 cm?
18. Find the perimeter of a rectangle that is 10 cm long and 5 cm wide.
19. A square has a perimeter of 12 cm. What is the length of each side?
20. Calculate the perimeter of a rectangle with a length of 6 cm and a width of 4 cm.

Medium Level Questions (20 questions)

1. A composite shape is made of a rectangle (length 10 cm, width 4 cm) and a square (side 5 cm). What is the perimeter?
2. Find the perimeter of a triangle with sides measuring 8 cm, 6 cm, and 10 cm.
3. If a rectangle has a perimeter of 30 cm and its length is 10 cm, what is its width?
4. A composite shape has two rectangles: one measuring 5 cm by 3 cm and another measuring 3 cm by 2 cm. What is the total perimeter?
5. Calculate the perimeter of a triangle that forms an isosceles triangle with two sides measuring 5 cm and the base measuring 8 cm.
6. Find the perimeter of a rectangle with a length of 12 cm and a width of 6 cm.
7. A square and a rectangle share one side. The square has a side of 4 cm, and the rectangle has a length of 8 cm and a width of 3 cm. What is the perimeter?
8. What is the perimeter of a triangle with sides measuring 10 cm, 10 cm, and 12 cm?
9. A composite shape consists of a rectangle (length 7 cm, width 3 cm) and a triangle (base 4 cm, height 3 cm). Find the perimeter.
10. Find the perimeter of a rectangle that is 9 cm long and 5 cm wide.
11. If the perimeter of a square is 40 cm, what is the length of one side?
12. A triangle has two sides of 7 cm each and a base of 10 cm. What is the perimeter?
13. Calculate the perimeter of a composite shape made of a rectangle (length 8 cm, width 5 cm) and a square (side 2 cm).
14. What is the perimeter of a rectangle with a length of 15 cm and a width of 10 cm?
15. A trapezium has bases measuring 5 cm and 7 cm, and the other two sides are both 4 cm. Find the perimeter.
16. Find the perimeter of a composite shape made up of a square (side 6 cm) and a rectangle (length 8 cm, width 4 cm).
17. If a rectangle has a perimeter of 40 cm, and its width is 10 cm, what is its length?
18. A triangle has sides measuring 9 cm, 12 cm, and 15 cm. What is the perimeter?
19. Calculate the perimeter of a shape made of a rectangle (length 4 cm, width 3 cm) and a triangle (base 5 cm, height 4 cm).
20. What is the perimeter of a composite shape made of two squares, each side measuring 3 cm?

Hard Level Questions (20 questions)

1. A composite shape consists of a rectangle (length 10 cm, width 5 cm) and a semicircle with a diameter of 5 cm. What is the total perimeter?
2. Find the perimeter of a triangle inscribed in a circle with a radius of 6 cm, where each side is equal to the diameter of the circle.
3. A trapezium has bases measuring 10 cm and 6 cm, and the non-parallel sides are 7 cm and 5 cm. What is the perimeter?
4. A composite shape has a rectangle (length 12 cm, width 6 cm) and a triangle (base 6 cm, height 8 cm). Find the total perimeter.
5. Calculate the perimeter of a composite shape made of a square (side 3 cm) and a rectangle (length 10 cm, width 4 cm).
6. A pentagon has sides measuring 3 cm, 4 cm, 5 cm, 6 cm, and 7 cm. What is its perimeter?
7. A hexagon has sides of equal length measuring 4 cm. Find its perimeter.
8. A composite shape is made of a rectangle (length 8 cm, width 5 cm) and a triangle (base 5 cm, height 5 cm). Calculate the total perimeter.
9. What is the perimeter of a shape formed by a rectangle (length 15 cm, width 7 cm) and a semicircle with a diameter of the rectangle’s width?
10. A shape consists of a rectangle (length 10 cm, width 4 cm) and a square (side 4 cm). What is the total perimeter?
11. A parallelogram has sides measuring 5 cm and 7 cm. What is its perimeter?
12. Find the perimeter of a composite shape made of a rectangle (length 5 cm, width 3 cm) and a triangle (base 5 cm, height 4 cm).
13. A rhombus has sides measuring 6 cm. What is its perimeter?
14. A composite shape is formed by a square (side 5 cm) and a triangle (base 5 cm, height 8 cm). Find the total perimeter.
15. A shape is made of a rectangle (length 12 cm, width 5 cm) and a quarter circle with a radius of 5 cm. Calculate the perimeter.
16. A kite has two pairs of equal adjacent sides measuring 6 cm and 8 cm. What is its perimeter?
17. Find the perimeter of a trapezium with bases of 10 cm and 6 cm, and non-parallel sides of 4 cm and 5 cm.
18. A composite shape consists of two squares, one with a side of 4 cm and the other with a side of 3 cm. What is the total perimeter?
19. Calculate the perimeter of a hexagon with sides measuring 2 cm, 3 cm, 4 cm, 5 cm, 6 cm, and 7 cm.
20. A cylinder has a radius of 3 cm. Calculate the perimeter of its base.

Answers

Easy Level Answers

1. 8 cm
2. 14 cm
3. 12 cm
4. 20 cm
5. 5 cm
6. 8 cm
7. 20 cm
8. 11 cm
9. 60 cm
10. 22 cm
11. 16 cm
12. 16 cm
13. 48 cm
14. 38 cm
15. 12 cm
16. 22 cm
17. 24 cm
18. 30 cm
19. 3 cm
20. 20 cm

Medium Level Answers

1. 38 cm
2. 24 cm
3. 5 cm
4. 26 cm
5. 23 cm
6. 36 cm
7. 24 cm
8. 32 cm
9. 30 cm
10. 28 cm
11. 10 cm
12. 24 cm
13. 35 cm
14. 26 cm
15. 48 cm
16. 24 cm
17. 20 cm
18. 28 cm
19. 14 cm
20. 18 cm

Hard Level Answers

1. 42.85 cm
2. 36 cm
3. 28 cm
4. 38 cm
5. 34 cm
6. 25 cm
7. 24 cm
8. 34 cm
9. 42.5 cm
10. 34 cm
11. 24 cm
12. 26 cm
13. 24 cm
14. 26 cm
15. 46.57 cm
16. 28 cm
17. 25 cm
18. 26 cm
19. 27 cm
20. 18.84 cm

Great job, Year 5! Keep practicing, and you’ll become experts in finding perimeters of composite shapes!