Units, Area & Perimeter

Mathematics· 5.1, 5.2· 15 min read

1. Metric Unit Conversions★★☆☆☆⏱ 4 min

Metric units follow a base-10 system. For linear (length) units, the conversion factor between adjacent units is 10. For area units, you square the linear conversion factor, and for volume/capacity you cube it. 1 litre = 1000 cm³ for capacity conversions.

📐 Worked Example

Convert 3.2 m² to cm².

1
Find the linear conversion factor between m and cm: 1 m = 100 cm
2
Square the linear factor for area: 1 m² = 100² = 10000 cm²
3
Multiply the given value by the conversion factor: 3.2 × 10000 = 32000 cm²

2. Perimeter of Standard 2D Shapes★★☆☆☆⏱ 3 min

Perimeter is the total distance around the edge of a closed 2D shape. For all shapes, you calculate it by adding the lengths of every outer side. For shapes with equal opposite sides (e.g. rectangles, parallelograms), you can simplify calculations using a formula.

📘 Definition

Perimeter

Sum of the lengths of all sides forming the boundary of a closed 2D shape

📐 Worked Example

Calculate the perimeter of a trapezium with side lengths 6 cm, 8 cm, 10 cm and 7 cm.

1
List all outer side lengths of the trapezium: 6, 8, 10, 7
2
Add all values together: 6 + 8 + 10 + 7 = 31 cm

3. Area of Quadrilaterals & Triangles★★★☆☆⏱ 5 min

Area is the amount of space occupied by a 2D shape, measured in square units. For Core tier exams, you must recall the area formulas for rectangles, parallelograms and trapeziums. The triangle area formula is provided on the exam formula sheet.

Shape	Area Formula	Must Recall?
Rectangle	$A = l \times w$	Yes
Parallelogram	$A = b \times h$ (h = perpendicular height)	Yes
Trapezium	$A = \frac{1}{2} (a + b) h$ (a,b = parallel sides, h = perpendicular height)	Yes
Triangle	$A = \frac{1}{2} \times b \times h$	No (given)

📐 Worked Example

Calculate the area of a parallelogram with base 9 cm and perpendicular height 4 cm.

1
Recall the parallelogram area formula: $A = ba se \times p er p e n d i c u l a r h e i g h t$
2
Substitute the given values: $A = 9 \times 4$
3
Calculate the final value: $A = 36$ cm²

Exam tip:

Always use the perpendicular height for area calculations, not the slant side of parallelograms or trapeziums.

4. Combined Exam Style Problems★★★☆☆⏱ 3 min

✓ Calculator OK

Most Core exam questions for this topic combine unit conversion with perimeter or area calculation. Always check the units required in the final answer before starting your working to avoid losing marks for incorrect units.

📐 Worked Example

A rectangular kitchen tile is 150 mm long and 100 mm wide. Calculate its area in cm².

1
First convert dimensions to cm: 150 mm = 15 cm, 100 mm = 10 cm
2
Use the rectangle area formula: $A = l \times w = 15 \times 10$
3
Final area = 150 cm²

5. Common Pitfalls

Wrong move:

Using linear conversion factor for area/volume calculations

Why:

Area uses 2 dimensions, volume uses 3, so the conversion factor must be adjusted accordingly

Correct move:

Square linear factor for area, cube for volume: e.g. 1 cm = 10 mm, so 1 cm² = 100 mm²

Wrong move:

Using slant height instead of perpendicular height for area calculations

Why:

Slant height is longer than perpendicular height, leading to overestimated area values

Correct move:

Always use the height measured at 90 degrees to the shape's base

Wrong move:

Forgetting to add one or more sides when calculating perimeter

Why:

Missing sides leads to undercalculated perimeter and lost method marks

Correct move:

Mark off each side as you add it to avoid double counting or omitting sides

Wrong move:

Using only one parallel side in the trapezium area formula

Why:

The trapezium area relies on the average length of the two parallel sides

Correct move:

Always add the two parallel sides first, multiply by height, then divide by 2

Wrong move:

Leaving final answer in wrong unit as specified in the question

Why:

Mixed units lead to incorrect numerical values and lost accuracy marks

Correct move:

Convert all values to the required unit at the start, or convert the final answer correctly at the end

6. Quick Reference Cheatsheet

Concept	Key Rule/Formula
Length conversion	1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm
Area conversion	Square linear factor: 1 m² = 10000 cm², 1 cm² = 100 mm²
Capacity conversion	1 litre = 1000 cm³, 1 m³ = 1000 litres
Rectangle area	$A = l e n g t h \times w i d t h$
Parallelogram area	$A = ba se \times p er p e n d i c u l a r h e i g h t$
Trapezium area	$A = \frac{1}{2} (a + b) h$
Perimeter	Sum of lengths of all outer sides of the shape

7. Frequently Asked

Do I get the trapezium area formula in the Core exam?

No. You must recall the rectangle, parallelogram and trapezium area formulas for Core tier. Only the triangle area formula is provided in the exam formula sheet.

How do I convert area units correctly?

Square the linear unit conversion factor for area calculations. For example, 1 cm = 10 mm, so 1 cm² = 10² = 100 mm².

Going deeper

syllabusCIE IGCSE Maths 0580 2025-2027 SyllabusOfficial syllabus document

What's Next

Now that you have mastered unit conversions, area and perimeter for Core tier, you can move on to more advanced mensuration topics in CIE IGCSE Maths 0580. Next, you will learn to calculate the area and circumference of circles, followed by volume of 3D shapes including prisms and cylinders. These skills build directly on the unit conversion and shape calculation basics you have learned here, and appear frequently in both Core and Extended exam papers. Be sure to practice past paper questions for this topic to avoid common unit conversion and formula recall mistakes before your exam.