Mensuration
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- Area uses square units and volume uses cubic units.
- Area of trapezium = 1/2 × sum of parallel sides × height.
- Volume of cuboid = lbh and cube = a³.
- Cylinder volume = πr²h.
- Convert all measurements to compatible units before using a formula.
What You Will Learn
- Find area of a trapezium
- Find area of a quadrilateral using a diagonal
- Find lateral and total surface areas
- Calculate volumes of cube, cuboid and cylinder
- Use correct square and cubic units
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
Area of trapezium
Use the two parallel sides and the perpendicular distance between them. The height is not a slant side.
Area of a quadrilateral
A general quadrilateral can be divided by a diagonal into two triangles. If perpendicular distances to that diagonal are known, add the two triangle areas.
Cuboid and cube
Surface area measures covering; volume measures capacity. Lateral surface area excludes top and bottom faces where appropriate.
Cylinder
Curved surface area covers only the curved side. Total surface area includes both circular bases.
Mensuration depends on identifying the correct dimensions.
Formula Sheet
Formula / Key Relations
Area of trapezium
a and b are parallel sides.
Quadrilateral using diagonal
h1 and h2 are perpendiculars to the diagonal.
Cuboid LSA
Four side faces.
Cuboid TSA
All six faces.
Cuboid volume
Use cubic units.
Cube TSA
All six square faces.
Cube volume
Use cubic units.
Cylinder CSA
Curved surface only.
Cylinder TSA
Curved surface plus two bases.
Cylinder volume
Base area × height.
Worked Examples
Area is 50 cm².
Volume is 1540 cm³.
Exam Traps
Quick Revision
Quick Revision
- Area uses square units and volume uses cubic units.
- Area of trapezium = 1/2 × sum of parallel sides × height.
- Volume of cuboid = lbh and cube = a³.
- Cylinder volume = πr²h.
- Convert all measurements to compatible units before using a formula.
- Revise the formula sheet once more before attempting questions.
Compact Practice
Area of trapezium with sides 8,12 and height 5?
View Solution
50 cm²
Volume of cube side 4 cm?
View Solution
64 cm³
Cuboid 5×3×2 volume?
View Solution
30 cm³
Cylinder r=3 cm, h=5 cm. Write volume expression.
View Solution
45π cm³
Final Chapter Summary
Chapter Summary
- Area uses square units and volume uses cubic units.
- Area of trapezium = 1/2 × sum of parallel sides × height.
- Volume of cuboid = lbh and cube = a³.
- Cylinder volume = πr²h.
- Convert all measurements to compatible units before using a formula.
- Prioritise correct method, clean working and final units where applicable.