Ch 1 · 5.1–5.2 Units of Measure, Area and Perimeter · IGCSE Mathematics 0580
Topic 1 of 3 in Mensuration — IGCSE Mathematics 0580 — 38 lessons.
Introduction
How much paint for a wall, how much fencing for a field, how many litres in a fish tank? Every answer needs the right formula and the right units. The trap in this topic is converting area and volume units, where 1 m is 100 cm but 1 m² is 10 000 cm². (Syllabus sections 5.1 and 5.2.)
Key ideas — Metric units
Volume and capacity: 1 cm³ = 1 ml, so 1000 cm³ = 1 l and 1 m³ = 1000 l.
🧑🏫 Teacher's explanation
Converting units is like changing your perspective. If you change how you measure a single line, you must change how you measure a flat surface or a 3D space accordingly. Imagine a square that is 1 m by 1 m. If you switch to centimeters, that square is 100 cm by 100 cm. The area isn't 100 cm^2; it is 100 × 100 = 10,000 cm^2.
📖 Definitions
🔍 Worked example — Easy
Convert 5.2 km into meters.
🔍 Worked example — Standard
A rectangular floor has an area of 12 m^2. Convert this area into cm^2.
🔍 Worked example — Exam-style
A water tank has a volume of 2.5 m^3. Calculate the capacity of the tank in litres (l).
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) Calculate the volume of the pool in m^3. (b) Calculate the capacity of the pool in litres (l). [3 marks]
Key ideas — Perimeter
The perimeter is the total distance around the outside: add all the side lengths (in the same units).
🧑🏫 Teacher's explanation
Imagine you are an ant walking along the very edge of a rectangular biscuit. The perimeter isn't the space where the chocolate is; it is the total distance your tiny legs travel to make one full lap around the edge. If you walk along one side and then turn the corner, you are still part of that same perimeter.
📖 Definitions
🔍 Worked example — Easy
Find the perimeter of a rectangle with a length of 8 cm and a width of 5 cm.
🔍 Worked example — Standard
A triangle has side lengths of 4.5 cm, 6 mm, and 5 cm. Calculate the perimeter in cm.
🔍 Worked example — Exam-style
A trapezium has parallel sides of 12 cm and 7 cm. The non-parallel sides are both 5 cm. Calculate the perimeter.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Area formulas
Only the triangle formula is given; the others must be learned. The height is always perpendicular to the base, not the sloping side.
🧑🏫 Teacher's explanation
Imagine you are tiling a floor. The perimeter is the length of the trim you need to go around the edges, but the area is the total number of tiles needed to cover the surface. When we talk about area, we are measuring how many 1 × 1 squares can fit inside a shape.
📖 Definitions
🔍 Worked example — Easy
Calculate the area of a rectangle with a length of 8 cm and a width of 5 cm.
🔍 Worked example — Standard
A triangle has a base of 12 m and a perpendicular height of 7 m. Calculate its area.
🔍 Worked example — Exam-style
A trapezium has parallel sides of lengths 10 cm and 16 cm. The perpendicular distance between them is 6 cm. Calculate the area. Give your answer in mm^2.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Worked examples
3.5 m² = 3.5 × 10 000 = 35 000 cm². A tank of 2.4 m³ holds 2.4 × 1000 = 2400 litres. 750 ml = 0.75 l.
🔍 Worked example — Easy
Convert 3.5 m^2 to cm^2.
🔍 Worked example — Standard
Calculate the area of a trapezium with parallel sides of 6 cm and 10 cm, and a perpendicular distance between them of 4 cm.
🔍 Worked example — Exam-style
A water tank has a volume of 2.4 m^3. Calculate its capacity in litres. (Note: 1 m^3 = 1000 litres)
⚠️ Common errors
Common mistakes
Practice
Answers: (1) 4.5 m². (2) 600 cm³. (3) tfrac12 × 12 × h = 42 ⇒ h = 7 cm. (4) perimeter 2(3.2 + 1.5) = 9.4 m; area 4.8 m².