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Lesson 5 of 10
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.
Lesson 5 of 10
New
New
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
- Different ways of decomposing the shape will give the same answer.
- The area stays the same however you split the shape.
- Calculate the areas of the rectangular parts and recombine to find the area of the whole shape.
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.
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?
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 (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
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6 Questions
Q1.To calculate the of a rectangle, multiply the length by the width.
To calculate the of a rectangle, multiply the length by the width.
Q2.What is the area of this square? cm².
What is the area of this square? cm².
Q3.Calculate the area of this rectangle. A = cm².
Calculate the area of this rectangle. A = cm².
Q4.What is the area of the lawn if the sides measure 13 m and 9 m?
What is the area of the lawn if the sides measure 13 m and 9 m?
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.
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.
Q6.The school hall measures 25 m by 9 m. What is the area of the hall floor? m².
The school hall measures 25 m by 9 m. What is the area of the hall floor? m².
Assessment exit quiz
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6 Questions
Q1.Match the start and end of the sentences to describe the shapes correctly.
Match the start and end of the sentences to describe the shapes correctly.
has all angles made from right angles.
is made up of two or more shapes.
Q2.Which times tables facts are needed to calculate the area of the shape?
Which times tables facts are needed to calculate the area of the shape?
8 × 8
10 × 6
Q3.Which times tables facts are needed to calculate the area of the shape?
Which times tables facts are needed to calculate the area of the shape?
6 × 8
10 × 6
Q4.True or false. These rectilinear shapes show the same area.
True or false. These rectilinear shapes show the same area.
False. The area of the shape is different.
Q5.Calculate the area of this rectilinear shape. m²
Calculate the area of this rectilinear shape. m²
Q6.Calculate the area of this rectilinear shape. m²
Calculate the area of this rectilinear shape. m²
