Mensuration

The art of measuring the world around us.

The Measuring Tape of the Universe

You know the properties of shapes and can construct them accurately. Now let us measure them — how much space they cover and how much they hold.

Welcome to the toolkit of the architect and the engineer. Mensuration is simply the 'how much' of the physical world: how much space a shape covers, how much it holds, and how long its edges are.

Formula

Think of mensuration as the measuring tape of mathematics — it turns abstract shapes into real numbers like square metres and litres.

Key idea

Curiosity spark: double every length of a box (width, depth and height) and it holds eight times as much. Size scales faster than you expect.

Memory trick

Measure twice, cut once — Mensuration is the math of 'How big is it?'

What You Will Learn

You will start by getting the units right, then measure flat shapes, then solids, and finish by breaking awkward composite shapes into pieces you already know.

Steps

1
Metric units, and converting between units of length, area and volume.
2
Perimeter and area: rectangle, triangle, parallelogram and trapezium.
3
Circles: circumference, area, arc length and the area of a sector.
4
Solids: surface area and volume of cuboids, cylinders, prisms, pyramids, cones and spheres.
5
Composite shapes: splitting a hard shape into easy ones and adding the pieces.

Formula

The one that covers every prism:

volume = area of cross-section \times length

Find the face that repeats, measure it, and push it along.

Practise mensuration now

Interactive visual aids, then real past-paper questions marked on your working like the exam. Free to start.

Practise free on Lemmara

Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education or Pearson Edexcel. The lessons and worked examples are Lemmara’s own.