Area, surface area and volume

The area of a triangle, the volume of a box and the surface area from a net. Read one step, play with it, then tap “I understand this”.

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The area of a triangle

Every triangle is exactly half of a rectangle with the same base and height. So: A = ½ × base × height.

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The triangle in the rectangle

Change the base and the height.

Watch out: which height?

The height is the straight up distance from the base to the top point (the red dotted line), not the slanted side.

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The volume of a box

Volume is how many 1 cm³ cubes fit in the box. Count one layer (length × width) and multiply by the number of layers (height): V = l × w × h.

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Pack the box

Change the length, width and height.

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Surface area with a net

Unfold a box and you get a net: six rectangles. The surface area is all six areas added together.

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The unfolded box

Change the box and look at the six faces.

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Cubes and litres

A cube has six equal square faces. With sides of s: V = s × s × s and SA = 6 × s × s.

Rule

1 cm³ = 1 mℓ, and 1 000 cm³ = 1 ℓ. A cube with sides of 10 cm holds exactly 1 litre.

Meerkat tip

Area has two dimensions (cm²). Volume has three (cm³). Always look at your units.

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Which formula?

Game

Work it out

Choose the right answer.

Correct: 0

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Check yourself

Remember this: your summary

Triangle: A = ½ × base × perpendicular height.
Rectangular prism: V = l × w × h.
Surface area: add the areas of all six faces.
Cube: V = s³, SA = 6 × s². 1 000 cm³ = 1 ℓ.

Write these points in your maths book. Read them again the night before the test.

Quiz

Quick questions

Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.

You ticked all 5 steps! Now you are ready for the quiz.

Free PDF to downloadPrint the practice sheet and practise on paper. The memo is on page 2: try on your own first.

Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
Measurement6 pages · PDFPaper Memo

All 14 free Grade 7 maths papers →

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For parents

One step a day is enough. Ten calm minutes work better than an hour the night before the test.
Unfold an empty cereal box together. Measure the six faces and add them up: that is the surface area.
Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.

Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.