Area of triangles, parallelograms and trapezia, and volume of cuboids
Every area formula for triangles, parallelograms and trapezia comes from the same trick: turning the shape into a rectangle you already know how to measure.
Part of your national curriculum
- Geometry and measures: Derive and apply formulae to calculate and solve problems involving perimeter and area of triangles, parallelograms and trapezia, and volume of cuboids
Lesson overview
What you'll learn in this lesson
Derive and apply formulae to calculate and solve problems involving perimeter and area of triangles, parallelograms and trapezia, and volume of cuboids
Key learning points
- • Key formulae
- • Worked example: triangle
- • Worked example: trapezium and cuboid
This lesson at a glance
- 28 minutes
- 16 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 16
Visual introductionPicture this
Area of triangles, parallelograms and trapezia, and volume of cuboids
Every area formula for triangles, parallelograms and trapezia comes from the same trick: turning the shape into a rectangle you already know how to measure.
In a nutshell
Derive and apply formulae to calculate and solve problems involving perimeter and area of triangles, parallelograms and trapezia, and volume of cuboids
Learning cycle
Part 2 of 16
Learning cycle 1 of 2
Part 1 · Key formulae
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 16
Learn
Key formulae
Triangle area = 1/2 × base × height. Parallelogram area = base × height. Trapezium area = 1/2 × (a + b) × height, where a and b are the parallel sides. Cuboid volume = length × width × height.
Reset break
Part 4 of 16
Pause
That's sitting 1 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 16
Learn
Worked example: triangle
A triangle has base 8 cm and height 5 cm. Area = 1/2 × 8 × 5 = 1/2 × 40 = 20 cm².
Quick check
Part 6 of 16
Quick check
Part 7 of 16
Quick check
A trapezium has parallel sides 6 cm and 10 cm, height 4 cm. What is its area?
Reset break
Part 8 of 16
Pause
That's sitting 2 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 16
Learning cycle 2 of 2
Part 2 · Worked example: trapezium and cuboid
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 16
Learn
Worked example: trapezium and cuboid
A trapezium has parallel sides 6 cm and 10 cm with height 4 cm: Area = 1/2 × (6+10) × 4 = 1/2 × 16 × 4 = 32 cm². A cuboid measuring 3 cm × 4 cm × 5 cm has volume 3×4×5 = 60 cm³.
Quick check
Part 11 of 16
Reset break
Part 12 of 16
Pause
That's sitting 3 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 13 of 16
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 14 of 16
Game · Recall cards
A triangle has base 8 cm and height 5 cm. What is its area?
Card 1 of 3
Mastery quiz
Part 15 of 16
Marked quiz
End of lesson quiz: Area of triangles, parallelograms and trapezia, and volume of cuboids
3 questions, marked with the reasoning shown. No timer.
1. A triangle has base 8 cm and height 5 cm. What is its area?
2. A trapezium has parallel sides 6 cm and 10 cm, height 4 cm. What is its area?
3. What is the volume of a cuboid 3 cm × 4 cm × 5 cm?
Lesson round-up
Part 16 of 16
Lesson round-up
Ready when you are
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Ask LunaPart 1 of 16 · Watch & discover
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Derive and apply formulae to calculate and solve problems involving perimeter and area of triangles, parallelograms and trapezia, and volume of cuboids