Composite shapes

Quick answer

Composite shapes are made by joining two or more simple shapes together. You can find their area or perimeter by splitting them into rectangles and adding up the parts.

Learning outcome

By the end of this page, you will be able to split a composite shape into rectangles, find the area or perimeter of each rectangle, and then add them together to find the total area or perimeter of the whole shape.

• You can identify when a shape is a composite shape.
• You can split a composite shape into rectangles.
• You can calculate the area or perimeter of each rectangle.
• You can add the areas or perimeters to find the total.

Why this matters

Composite shapes are everywhere around you! When you are building with LEGO, drawing a garden, or even planning a party, you often use shapes that are made from combining smaller shapes. Knowing how to break down these shapes helps you solve problems like: How much paint do I need for my room? How much fencing do I need for my garden? Understanding composite shapes helps you become a better problem solver and makes math more useful in real life.

How it works

Composite shapes are made by joining two or more simple shapes together. To find the area or perimeter of a composite shape, follow these steps:

1. Look at the shape and see how many simple shapes it is made from.
2. Split it into rectangles – draw lines or imagine lines to separate it into rectangles.
3. Find the area or perimeter of each rectangle.
4. Add them together to get the total area or perimeter.

Examples you can see

Let’s look at a simple example. Imagine a shape that looks like a letter L. This shape can be split into two rectangles.

Example 1: Finding the area of an L-shaped composite shape

Imagine an L-shaped shape made from two rectangles:

• Rectangle A is 5 cm long and 3 cm wide.
• Rectangle B is 3 cm long and 2 cm wide.

To find the total area:

1. Area of Rectangle A = 5 cm × 3 cm = 15 cm²
2. Area of Rectangle B = 3 cm × 2 cm = 6 cm²
3. Total area = 15 cm² + 6 cm² = 21 cm²

Example 2: Finding the perimeter of a T-shaped composite shape

Imagine a T-shaped composite shape made from two rectangles:

• Top rectangle: 4 cm long and 1 cm wide.
• Bottom rectangle: 4 cm long and 2 cm wide, placed directly below the top one.

To find the perimeter, we need to add up all the sides:

1. Top rectangle: 4 + 1 + 4 + 1 = 10 cm
2. Bottom rectangle: 4 + 2 + 4 + 2 = 12 cm
3. Total perimeter = 10 cm + 12 cm = 22 cm

But wait! Some sides are shared, so we have to be careful. The actual perimeter is the outside edges only:

• Top rectangle: 4 + 1 + 4 + 1 = 10 cm
• Bottom rectangle: 4 + 2 + 4 + 2 = 12 cm
• Shared side = 4 cm (we subtract this once)
• Total perimeter = 10 + 12 – 4 = 18 cm

Try it as a mini adventure

Adventure: The Garden Planner

You are a garden designer and you need to plan a new garden. Your garden is shaped like a composite shape – it has a square section and a rectangular section. The square is 5 m by 5 m, and the rectangle is 5 m long and 3 m wide.

1. Split the garden into two rectangles.
2. Find the area of each rectangle.
3. Add the areas together to find the total garden area.
4. How much fencing do you need to go around the whole garden?

Draw your garden on paper and label each part. Then calculate the total area and perimeter!

Common mistakes

• Mistake: Forgetting to split the shape into rectangles.
  Why it happens: The shape looks too complicated.
  Fix: Draw lines to separate it into rectangles. Look for right angles and straight edges.
• Mistake: Adding the areas or perimeters of rectangles that overlap or share sides.
  Why it happens: Not paying attention to which sides are inside or outside.
  Fix: Only count the outside edges when finding perimeter. Make sure you don’t double-count shared sides.
• Mistake: Using the wrong formula for area or perimeter.
  Why it happens: Mixing up rectangle area (length × width) with perimeter (2 × (length + width)).
  Fix: Remember: Area = length × width. Perimeter = add all sides.

Parent and carer guide

Helping your child understand composite shapes is easy and fun!

• Start with simple shapes: Use paper and scissors to cut out rectangles and make your own composite shapes.
• Use real-life examples: Look at your home. What shapes can you see that are made of rectangles? A bookshelf, a window, a door.
• Draw and label: Encourage your child to draw the shape, split it into rectangles, and write the measurements.
• Ask questions: “How many rectangles are in this shape?” “What is the area of this part?”
• Don’t rush: Composite shapes can be tricky at first, so take your time and make it a fun activity.

Remember: It’s okay if your child makes mistakes. They are part of the learning process. Keep the atmosphere light and encouraging!

Practice questions

1. Split a composite shape made of two rectangles: one 6 cm by 4 cm, and another 4 cm by 3 cm. What is the total area?
2. A composite shape has a rectangle 5 cm by 2 cm and a square 3 cm by 3 cm. What is the total perimeter?
3. How many rectangles can you see in a shape that looks like a T? What is the area of each if the top is 4 cm by 1 cm and the bottom is 4 cm by 2 cm?
4. Find the area of a shape made from a 3 cm by 5 cm rectangle and a 2 cm by 5 cm rectangle joined side by side.
5. What is the perimeter of a shape made from a 6 cm by 3 cm rectangle and a 3 cm by 3 cm rectangle joined side by side?

Answers:

1. Area = (6 × 4) + (4 × 3) = 24 + 12 = 36 cm²
2. Perimeter = (5 + 2 + 5 + 2) + (3 + 3 + 3 + 3) = 14 + 12 = 26 cm
3. Two rectangles. Top area = 4 × 1 = 4 cm². Bottom area = 4 × 2 = 8 cm².
4. Area = (3 × 5) + (2 × 5) = 15 + 10 = 25 cm²
5. Perimeter = (6 + 3 + 6 + 3) + (3 + 3 + 3 + 3) = 18 + 12 = 30 cm

FAQ

What is a composite shape?

A composite shape is a shape made by joining two or more simple shapes together, like rectangles or squares.

Why do we split composite shapes?

Splitting them makes it easier to find their area or perimeter because we can calculate each rectangle separately and then add the results.

Can I split a composite shape in more than one way?

Yes! You can split it in different ways, as long as the parts are all rectangles and you add up the correct measurements.

Do I always need to find the area or perimeter?

No! You can split a composite shape to find either area or perimeter, depending on what you need to solve.

How can I practice this at home?

You can draw composite shapes, cut them out, and measure them. Try to find the area of your bedroom or the perimeter of your garden!