© Crown copyright 2023. This information is licensed under the Open Government Licence (nationalarchives.gov.uk) v 3.0 1
Lesson plan
Area and perimeter of
rectilinear shapes and
compound shapes
1. Lesson objectives
• Explore the area and perimeter of squares, rectangles, triangles and compound
shapes
• Understand the concepts of area and perimeter and use them in a range of
problem-solving situations
2. GCSE curriculum
Geometry and measures
G14 use standard units of measure and related concepts (length, area,
volume/capacity, mass, time, money, etc.)
G16 know and apply formulae to calculate area of triangles, parallelograms, trapezia;
volume of cuboids and other right prisms (including cylinders)
G17 know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr
2
;
calculate: perimeters of 2D shapes, including circles; areas of circles and composite
shapes; surface area and volume of spheres, pyramids, cones and composite solids
© Crown copyright 2023. This information is licensed under the Open Government Licence (nationalarchives.gov.uk) v 3.0 2
3. Lesson plan
This is an overview of the lesson. More notes can be found in the notes in the lesson slides.
Activity
Purpose of this
activity
Time
(min)
Guidance
Materials
Introduction
To highlight how
changes in length
versus changes in
width affect the
area of a rectangle
10
Introduce the concept of area of rectangles. Ask learners to
work in pairs to consider two statements relating to how
changes to the dimensions of three fields affect the areas.
Gather responses from the learners.
Slides 2–3
‘Three
gardens’
handout
Discuss 1
To explore area and
perimeter (including
factors and square
numbers)
10
Ask learners to work independently to draw various rectangles
on a dot grid and note their observations about the dimensions
of the rectangles.
Teacher to get feedback from students and use various
squares to elicit and demonstrate important concepts relating to
squares, area, and perimeter.
Ask learners to consider a set of statements and decide which
statement is incorrect. Address misconceptions in the incorrect
statements.
Slides 4–8
Dot grid paper
Discuss 2
To demonstrate
how the formula for
the area of a
triangle is derived
and highlight
common
misconceptions
15
Use the visuals on the slides to show a rectangle split into two
triangles. Guide learners to derive the formula for the area of a
triangle.
Ask learners to consider a set of statements and work out what
mistakes were made, and which is the correct answer. Address
misconceptions in the incorrect statements.
Slide 9–11
© Crown copyright 2023. This information is licensed under the Open Government Licence (nationalarchives.gov.uk) v 3.0 3
Activity
Purpose of this
activity
Time
(min)
Guidance
Materials
Explore 1
To solve problems
involving the area of
compound shapes
10
Ask learners to work in pairs to work out the area of two
compound shapes. Once learners have completed the task,
ask some pairs to share the different methods to find the areas
of each of the shapes.
Slides 12–16
‘Area of
compound
shapes’
handout
Calculators
Explore 2
To solve multi-step
problems involving
area of compound
shapes
25
Ask learners to work in pairs to work out which venue has the
greatest area and will make the most income for a music event.
Slides 17–22
‘Crowd
capacity’
handout
Practice
question
Learners check and
consolidate their
understanding by
answering exam
questions
15
Ask learners to answer exam questions and after a few minutes
discuss their thinking.
Slides 23–25
‘Practice
questions’
handout
Review
To summarise
learning and review
the concept of
areas and
perimeters of
various shapes
5
Recap the learning points of the lessons.
Slide 26
