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Geometry and mensuration

Use angle facts and metric formulae for perimeter, area, surface area and volume.

12 free questions · Notes · Worked solutions

Practise this topic

What you will practise

  • Apply angle rules for lines, triangles and polygons.
  • Calculate perimeter and area of common 2D shapes.
  • Calculate circumference, circle area and volume.
  • Convert units and use formulae with accurate rounding.

Revision notes

Angle facts

Angles on a straight line total 180°, around a point total 360°, and vertically opposite angles are equal. A triangle totals 180°; an exterior angle equals the sum of the two opposite interior angles.

Area and circumference

Rectangle area=length×width; triangle area=½×base×perpendicular height; parallelogram area=base×perpendicular height. For a circle, circumference=2πr and area=πr².

Volume

A prism has volume=area of cross-section×length. A cuboid has volume=lwh. A cylinder has volume=πr²h. Surface area is the total area of its exposed faces.

Units and checks

Area uses squared units; volume uses cubed units. Convert lengths before substituting into one formula. Radius is half the diameter. Check whether an answer is a perimeter, area or volume.

A worked example

A circular pond has radius 3 m. Find its area and circumference in terms of π.

  1. The radius is r=3 m.
  2. Area=πr²=π×3²=9π m².
  3. Circumference=2πr=2π×3=6π m.

Area 9π m²; circumference 6π m

Try it yourself

These are original practice questions, not official past-paper questions. Practice points count correct final answers; working is not automatically assessed.

Choose a question to begin.
Question 1 · Standard1 practice point

Two angles on a straight line are x° and 127°. Find x.

Need a hint?

Angles on a straight line total 180°.

Worked solution
  1. x+127=180.
  2. x=53°.
Question 2 · Standard1 practice point

A triangle has angles 48° and 67°. Find the third angle.

Need a hint?

The interior angles of a triangle total 180°.

Worked solution
  1. 48+67=115.
  2. 180−115=65°.
Question 3 · Standard1 practice point

A rectangle measures 9 cm by 4 cm. What is its area?

Need a hint?

Multiply length by width.

Worked solution
  1. Area=9×4=36 cm².
Question 4 · Standard1 practice point

A circle has diameter 10 cm. What is its circumference in terms of π?

Need a hint?

Circumference is π times diameter.

Worked solution
  1. C=πd=10π cm.
Question 5 · Foundation1 practice point

Find the perimeter of a square with side length 7.5 cm.

Need a hint?

A square has four equal sides.

Worked solution
  1. Perimeter=4×7.5.
  2. Perimeter=30 cm.
Question 6 · Foundation2 practice points

A triangle has base 12 cm and perpendicular height 7 cm. Find its area.

Need a hint?

Use one half times base times perpendicular height.

Worked solution
  1. Area=½×12×7.
  2. Area=42 cm².
Question 7 · Standard2 practice points

Find the circumference of a circle with radius 5 cm. Give your answer to 1 decimal place, using π=3.142.

Need a hint?

Use C=2πr.

Worked solution
  1. C=2×3.142×5=31.42 cm.
  2. To 1 decimal place, C=31.4 cm.
Question 8 · Standard2 practice points

A cuboid is 8 cm long, 3 cm wide and 5 cm high. Find its volume.

Need a hint?

Multiply the three perpendicular dimensions.

Worked solution
  1. V=8×3×5.
  2. V=120 cm³.
Question 9 · Foundation1 practice point

A regular hexagon has perimeter 54 cm. Find the length of one side.

Need a hint?

A regular hexagon has six equal sides.

Worked solution
  1. Side=54÷6.
  2. Side=9 cm.
Question 10 · Standard2 practice points

Find the area of a circle of radius 4 cm, using π=3.14.

Need a hint?

Square the radius before multiplying by π.

Worked solution
  1. A=πr²=3.14×4².
  2. A=3.14×16=50.24 cm².
Question 11 · Stretch3 practice points

A rectangular floor is 4.2 m long and 350 cm wide. Find its area in m².

Need a hint?

Convert 350 cm to metres first.

Worked solution
  1. 350 cm=3.5 m.
  2. Area=4.2×3.5.
  3. Area=14.7 m².
Question 12 · Stretch3 practice points

A cylinder has radius 2 cm and height 10 cm. Find its volume using π=3.14.

Need a hint?

Use V=πr²h.

Worked solution
  1. V=3.14×2²×10.
  2. V=3.14×4×10=125.6 cm³.

Coverage and sources

Selected IGCSE concepts, with a mix of introductory and more demanding questions. Check your own specification. AI drafted; independent teacher review is pending. Editorial details.

Cambridge IGCSE Mathematics 0580 syllabus

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