Good Learning Co.
SavannahYear 8
← Maths
MathsShape and space28 min★★ difficulty

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
  • 13 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

deriveformulaecalculateproblemsinvolving

Scroll down — the lesson carries on below

Part 1 of 13 · Discover8%
1

Watch & discover

Part 1 of 13

Watch first

Area of triangles, parallelograms and trapezia, and volume of cuboids

An English teaching video on this topic from Homeschool Pop. Watch it, then scroll down for the lesson.

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

2

Learning cycle

Part 2 of 13

Learning cycle 1 of 2

Part 1 · Key formulae

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 13

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.

4

Explore the idea

Part 4 of 13

Learn

Worked example: triangle

A triangle has base 8 cm and height 5 cm. Area = 1/2 × 8 × 5 = 1/2 × 40 = 20 cm².

5

Quick check

Part 5 of 13

Quick check

A triangle has base 8 cm and height 5 cm. What is its area?

6

Reset break

Part 6 of 13

Pause

That's sitting 1 of 2 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.

Stop here for now
7

Quick check

Part 7 of 13

Quick check

A trapezium has parallel sides 6 cm and 10 cm, height 4 cm. What is its area?

8

Learning cycle

Part 8 of 13

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.

9

Explore the idea

Part 9 of 13

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.

10

Quick check

Part 10 of 13

Quick check

What is the volume of a cuboid 3 cm × 4 cm × 5 cm?

11

Challenge round

Part 11 of 13

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

12

Mastery quiz

Part 12 of 13

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. 1. A triangle has base 8 cm and height 5 cm. What is its area?

  2. 2. A trapezium has parallel sides 6 cm and 10 cm, height 4 cm. What is its area?

  3. 3. What is the volume of a cuboid 3 cm × 4 cm × 5 cm?

13

Lesson round-up

Part 13 of 13

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

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Points this lesson

0

Best run

0 in a row

Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 13 · 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

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