Year 5 Maths: Area of Composite Shapes

Introduction to Composite Shapes

Hello, Year 5! Today, we’re going to learn about something exciting in maths: composite shapes! But what is a composite shape?

A composite shape is a shape that is made up of two or more simple shapes. Simple shapes can include rectangles, squares, triangles, and circles. By understanding how to find the area of these simple shapes, we can also find the area of more complicated, composite shapes.

Finding the Area of Simple Shapes

Before we tackle composite shapes, let’s quickly review how to find the area of some simple shapes:

Rectangle

To find the area of a rectangle, use this formula:

$$\text{Area} = \text{length} \times \text{width}$$

Square

For a square, since all sides are equal, the formula is:

$$\text{Area} = \text{side} \times \text{side}$$

Triangle

For a triangle, we use this formula:

$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$

Circle

Lastly, for a circle, the area is found with:

$$\text{Area} = \pi \times \text{radius}^2$$

(Here, ( \pi ) is about 3.14, but you can often use 3.14 for calculations.)

How to Find the Area of Composite Shapes

Now, let’s learn how to find the area of composite shapes! Here’s a step-by-step guide:

1. Identify the Simple Shapes: Look at the composite shape and see which simple shapes make it up.
2. Calculate Each Area: Use the formulas for each simple shape to find their areas.
3. Add or Subtract Areas: If you are combining shapes, add their areas together. If one shape is cut out from another, subtract the area of the smaller shape from the larger shape.

Example 1: Composite Shape Made of Rectangles

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

• Rectangle: Length = 5 cm, Width = 3 cm
• Square: Side = 2 cm

Step 1: Find the area of the rectangle.

$$

\text{Area}_{\text{rectangle}} = 5 \times 3 = 15 , \text{cm}^2

$$

Step 2: Find the area of the square.

$$

\text{Area}_{\text{square}} = 2 \times 2 = 4 , \text{cm}^2

$$

Step 3: Add the areas together.

$$

\text{Total Area} = 15 + 4 = 19 , \text{cm}^2

$$

Example 2: Composite Shape with a Cut-Out

Now, let’s say we have a rectangle with a triangle cut out of it.

• Rectangle: Length = 6 cm, Width = 4 cm
• Triangle: Base = 4 cm, Height = 3 cm

Step 1: Find the area of the rectangle.

$$

\text{Area}_{\text{rectangle}} = 6 \times 4 = 24 , \text{cm}^2

$$

Step 2: Find the area of the triangle.

$$

\text{Area}_{\text{triangle}} = \frac{1}{2} \times 4 \times 3 = 6 , \text{cm}^2

$$

Step 3: Subtract the area of the triangle from the rectangle.

$$

\text{Total Area} = 24 – 6 = 18 , \text{cm}^2

$$

Tips and Tricks

• Draw It Out: Always draw the shape and label the dimensions. This will help you see the simple shapes better.
• Check Your Work: After calculating the areas, double-check your addition or subtraction.
• Practice: The more you practice, the easier it will become!

Questions

Easy Level Questions

1. What is the area of a rectangle with a length of 4 cm and a width of 3 cm?
2. Find the area of a square with a side of 5 cm.
3. Calculate the area of a triangle with a base of 6 cm and a height of 2 cm.
4. What is the area of a rectangle with a length of 8 cm and a width of 2 cm?
5. Find the area of a square with a side of 4 cm.
6. What is the area of a circle with a radius of 3 cm? (Use 3.14 for π)
7. If a rectangle has a length of 10 cm and a width of 5 cm, what is its area?
8. Find the area of a triangle with a base of 5 cm and height of 5 cm.
9. What is the area of a square with a side of 6 cm?
10. Calculate the area of a rectangle with length 12 cm and width 1 cm.
11. If a rectangle has a length of 7 cm and a width of 4 cm, what is its area?
12. What is the area of a triangle with a base of 8 cm and height of 4 cm?
13. Find the area of a square with a side of 3 cm.
14. What is the area of a rectangle with a length of 9 cm and a width of 3 cm?
15. If a square has an area of 16 cm², what is the length of one side?
16. Find the area of a triangle with a base of 10 cm and height of 2 cm.
17. What is the area of a rectangle with a length of 6 cm and a width of 6 cm?
18. Calculate the area of a square with a side of 7 cm.
19. If a rectangle has a length of 5 cm and width of 5 cm, what is its area?
20. What is the area of a triangle with a base of 7 cm and a height of 3 cm?

Medium Level Questions

1. Find the area of a composite shape made of a rectangle (length 5 cm, width 3 cm) and a square (side 2 cm).
2. Calculate the total area of a rectangle with a length of 10 cm and a width of 4 cm, plus a triangle with a base of 4 cm and height of 3 cm.
3. What is the area of a composite shape made of a rectangle (length 6 cm, width 2 cm) and a circle (radius 1 cm)?
4. Find the area of a rectangle (length 8 cm, width 5 cm) and subtract the area of a square (side 3 cm).
5. Calculate the area of a rectangle (length 12 cm, width 3 cm) combined with a triangle (base 6 cm, height 4 cm).
6. What is the area of a rectangle (length 7 cm, width 3 cm) and a triangle (base 3 cm, height 3 cm)?
7. Find the area of a rectangle (length 10 cm, width 6 cm) minus a square (side 2 cm).
8. Calculate the total area of a rectangle (length 5 cm, width 4 cm) and a triangle (base 4 cm, height 2 cm).
9. What is the area of a composite shape made of a square (side 4 cm) and a rectangle (length 4 cm, width 2 cm)?
10. Find the area of a rectangle (length 9 cm, width 2 cm) and a circle (radius 2 cm).
11. Calculate the area of a rectangle (length 6 cm, width 5 cm) plus a triangle (base 5 cm, height 5 cm).
12. What is the area of a rectangle (length 11 cm, width 3 cm) and a triangle (base 5 cm, height 2 cm)?
13. Find the area of a composite shape made of a rectangle (length 10 cm, width 4 cm) and a square (side 5 cm).
14. Calculate the total area of a rectangle (length 8 cm, width 3 cm) combined with a triangle (base 6 cm, height 3 cm).
15. What is the area of a rectangle (length 7 cm, width 5 cm) minus a square (side 3 cm)?
16. Find the area of a rectangle (length 12 cm, width 6 cm) and a triangle (base 4 cm, height 2 cm).
17. Calculate the area of a rectangle (length 10 cm, width 2 cm) and a circle (radius 3 cm).
18. What is the area of a composite shape made of a square (side 5 cm) and a rectangle (length 5 cm, width 3 cm)?
19. Find the area of a rectangle (length 9 cm, width 4 cm) and subtract the area of a triangle (base 4 cm, height 3 cm).
20. Calculate the area of a rectangle (length 8 cm, width 3 cm) plus a triangle (base 5 cm, height 4 cm).

Hard Level Questions

1. Find the area of a composite shape with a rectangle (length 8 cm, width 4 cm) and a triangle (base 6 cm, height 3 cm) subtracted from it.
2. Calculate the total area of a rectangle (length 10 cm, width 5 cm) and a semicircle (diameter 6 cm).
3. What is the area of a composite shape made of a square (side 5 cm) and a triangle (base 4 cm, height 3 cm) subtracted from the square?
4. Find the area of a rectangle (length 12 cm, width 8 cm) and subtract the area of a triangle (base 6 cm, height 4 cm).
5. Calculate the area of a composite shape with a rectangle (length 10 cm, width 5 cm) and a circle (radius 2 cm).
6. What is the area of a rectangle (length 15 cm, width 5 cm) minus a triangle (base 9 cm, height 4 cm)?
7. Find the area of a composite shape made of a rectangle (length 10 cm, width 6 cm) and a trapezium (base1 6 cm, base2 4 cm, height 3 cm).
8. Calculate the total area of a rectangle (length 14 cm, width 5 cm) and a triangle (base 10 cm, height 4 cm).
9. What is the area of a composite shape with a square (side 6 cm) and a rectangle (length 5 cm, width 4 cm) added together?
10. Find the area of a rectangle (length 20 cm, width 10 cm) and subtract the area of a triangle (base 10 cm, height 8 cm).
11. Calculate the area of a composite shape made of a rectangle (length 15 cm, width 5 cm) and a circle (radius 3 cm).
12. What is the area of a rectangle (length 9 cm, width 7 cm) minus the area of a triangle (base 6 cm, height 3 cm)?
13. Find the area of a composite shape with a rectangle (length 10 cm, width 4 cm) and a semicircle (diameter 8 cm).
14. Calculate the total area of a rectangle (length 12 cm, width 6 cm) and a triangle (base 4 cm, height 3 cm).
15. What is the area of a rectangle (length 14 cm, width 3 cm) plus a triangle (base 8 cm, height 4 cm)?
16. Find the area of a composite shape made of a square (side 8 cm) and a rectangle (length 6 cm, width 4 cm).
17. Calculate the area of a rectangle (length 15 cm, width 9 cm) and a triangle (base 10 cm, height 2 cm).
18. What is the area of a rectangle (length 13 cm, width 6 cm) minus the area of a triangle (base 7 cm, height 5 cm)?
19. Find the area of a composite shape with a rectangle (length 10 cm, width 4 cm) and a trapezium (base1 5 cm, base2 3 cm, height 4 cm).
20. Calculate the total area of a rectangle (length 20 cm, width 10 cm) and a circle (radius 5 cm).

Answers and Explanations

Easy Level Answers

1. 12 cm²
2. 25 cm²
3. 6 cm²
4. 16 cm²
5. 16 cm²
6. 28.26 cm²
7. 50 cm²
8. 12 cm²
9. 16 cm²
10. 12 cm²
11. 28 cm²
12. 6 cm²
13. 9 cm²
14. 27 cm²
15. 4 cm
16. 10 cm²
17. 36 cm²
18. 25 cm²
19. 21 cm²
20. 10.5 cm²

Medium Level Answers

1. 19 cm²
2. 36 cm²
3. 35.14 cm²
4. 31 cm²
5. 48 cm²
6. 30.5 cm²
7. 58 cm²
8. 24 cm²
9. 16 cm²
10. 38.26 cm²
11. 51 cm²
12. 38 cm²
13. 47 cm²
14. 41 cm²
15. 37 cm²
16. 78.26 cm²
17. 66 cm²
18. 42 cm²
19. 22 cm²
20. 24 cm²

Hard Level Answers

1. 21 cm²
2. 65.28 cm²
3. 12.5 cm²
4. 34 cm²
5. 63.42 cm²
6. 41 cm²
7. 84 cm²
8. 66 cm²
9. 42 cm²
10. 92 cm²
11. 67.34 cm²
12. 36 cm²
13. 50.26 cm²
14. 39 cm²
15. 50 cm²
16. 70 cm²
17. 65 cm²
18. 26.5 cm²
19. 64 cm²
20. 252.5 cm²

I hope this helps you understand composite shapes better! Remember to take your time while solving problems, and don’t hesitate to ask for help if you need it. Happy learning!