Area of triangles, parallelograms and trapeziums – Year 9 maths lesson
Lesson 8 of 38 in the Year 9 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 9 (ages 13–14) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 9 (ages 13–14)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why does a triangle's area formula have ½ in it?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using the slanted side instead of the perpendicular height. The height must meet the base at a right angle.
- Forgetting the ½ for a triangle. A triangle is half a parallelogram.
Tip for home: Work out the area of a garden or room with an awkward shape.
What your child will learn
We are learning to find the area of triangles, parallelograms, trapeziums and compound shapes.
Success looks like
- I can find the area of a triangle and a parallelogram.
- I can find the area of a trapezium.
- I can find the area of compound shapes.
Key words
- area
- the space inside a flat shape
- perpendicular height
- the height at right angles to the base
- parallelogram
- a quadrilateral with two pairs of parallel sides
- trapezium
- a quadrilateral with one pair of parallel sides
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Cut a parallelogram from paper and rearrange it into a rectangle to see why base × height works.
The big ideas (for the adult)
Area of a parallelogram = base × perpendicular height. Area of a triangle = ½ × base × perpendicular height.
Area of a trapezium = ½ × (a + b) × h, where a and b are the parallel sides.
For a compound shape, split it into simple shapes, find each area and add (or subtract a missing part).
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 9 maths lessons
- Prime factors, HCF and LCM
- Rounding and estimation
- Bounds and error intervals
- Standard form
- Laws of indices
- Powers and roots
- Units and measures
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Angle facts and parallel lines
- Angles in polygons
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Quadrilaterals and symmetry
- Coordinate geometry
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Pie charts and time series graphs
- Sampling
- Relative frequency and expected outcomes
- Venn diagrams and conditional probability
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Inequalities
- Rearranging formulae
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Speed, density and pressure
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 9: “derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)”
National Curriculum for England, Year 9: “interpret mathematical relationships both algebraically and geometrically”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.