New
New
Year 5

Calculate the area of shapes made from 2 rectangles by decomposing the shape in different ways

You can decompose or split shapes into rectangles in different ways.

New
New
Year 5

Calculate the area of shapes made from 2 rectangles by decomposing the shape in different ways

You can decompose or split shapes into rectangles in different ways.

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Lesson details

Key learning points

  1. Different ways of decomposing the shape will give the same answer.
  2. The area stays the same however you split the shape.
  3. Calculate the areas of the rectangular parts and recombine to find the area of the whole shape.

Common misconception

Some pupils may not see that two rectilinear shapes can look very different but have the same area.

Cut out a large rectangle. Cut it into two rectangles. Ask pupils to move one of the rectangles and reposition it. Has the area changed?

Keywords

  • Rectilinear - A shape made up of two or more rectangles is known as rectilinear.

  • Compound - A compound shape is one made up of two or more shapes.

Some pupils may need extra practice with working out the area of compound shapes where the rectangles are not pre-marked before they move onto example requiring them to divide the shape into rectangles.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
To calculate the of a rectangle, multiply the length by the width.
Correct Answer: area, Area
Q2.
What is the area of this square? cm².
An image in a quiz
Correct Answer: 81, 81 cm², 81 centimetres squared, 81 square centimentres
Q3.
Calculate the area of this rectangle. A = cm².
An image in a quiz
Correct Answer: 105, 105 cm², 105 centimetres squared, 105 square centimetres
Q4.
What is the area of the lawn if the sides measure 13 m and 9 m?
Correct Answer: 117, 117 m², 117 metres squared, 117 square metres
Q5.
A picture is put into a frame that is 17cm long and 8 cm wide. What is the area of the glass in the frame? cm².
Correct Answer: 136, 136 cm², 136 square centimetres, 136 centimetres squared
Q6.
The school hall measures 25 m by 9 m. What is the area of the hall floor? m².
Correct Answer: 225 , 225 m², 225 square centimetres, 225 centimetres squared

6 Questions

Q1.
Match the start and end of the sentences to describe the shapes correctly.
Correct Answer:A rectilinear shape ,has all angles made from right angles.

has all angles made from right angles.

Correct Answer:A compound shape ,is made up of two or more shapes.

is made up of two or more shapes.

Q2.
Which times tables facts are needed to calculate the area of the shape?
An image in a quiz
Correct answer: 10 × 8
8 × 8
Correct answer: 6 × 8
10 × 6
Q3.
Which times tables facts are needed to calculate the area of the shape?
An image in a quiz
Correct answer: 8 × 8
6 × 8
10 × 6
Correct answer: 8 × 8
Q4.
True or false. These rectilinear shapes show the same area.
An image in a quiz
Correct answer: True. The smaller rectangle has changed position.
False. The area of the shape is different.
Q5.
Calculate the area of this rectilinear shape.
An image in a quiz
Correct Answer: 72, 72 m², 72 metres squared, 72 square metres
Q6.
Calculate the area of this rectilinear shape.
An image in a quiz
Correct Answer: 129, 129 cm², 129 centimetres squared, 129 square centimetres