Area of triangles, parallelograms and trapezoids – Grade 7 math lesson
Lesson 13 of 21 in the Grade 7 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 7 (ages 12–13) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 7 (ages 12–13)
- You need
- Paper, a pencil and this page
- Graded
- 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 graded straight away with a worked explanation, so you never have to grade 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
Learning goal: find the area of triangles, parallelograms, trapezoids and composite 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
- trapezoid
- 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 trapezoid = ½ × (a + b) × h, where a and b are the parallel sides.
For a composite 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 | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded 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 graded instantly.
More practice
More Grade 7 math lessons
- Ratios
- Percent
- Proportional relationships
- Operations with integers
- Repeating decimals
- Evaluating expressions
- Simplifying expressions
- Expanding expressions
- Solving equations
- Inequalities
- Scale drawings and maps
- Angle relationships
- Circles: circumference and area
- Volume and surface area
- Cross sections of 3-D figures
- Probability
- Experimental probability
- Compound events
- Box plots and interquartile range
- Sampling and making inferences
Curriculum
Common Core State Standards 7.G.B.6: “Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.”
Common Core State Standards HSG.MG.A.3: “Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.