Area, Perimeter and Volume: A Junior Cycle Maths Guide
Quick answer: Perimeter is the distance around a shape, measured in units like cm. Area is the space inside a flat shape, in square units like cm². Volume is the space inside a 3D shape, in cubic units like cm³. Most Junior Cycle questions come down to choosing the right formula, substituting carefully and giving the right units. Compound shapes are usually split into simpler shapes, then added or subtracted.
Area and perimeter formulas
Rectangle: area = length × width · perimeter = 2(length + width)
Square: area = side² · perimeter = 4 × side
Triangle: area = ½ × base × perpendicular height · perimeter = sum of the three sides
Parallelogram: area = base × perpendicular height · perimeter = sum of the four sides
Circle: area = πr² · circumference = 2πr (or πd)
Volume and surface area formulas
Cuboid: volume = length × width × height · surface area = 2(lw + lh + wh)
Cylinder: volume = πr²h · curved surface area = 2πrh
Cone: volume = ⅓πr²h · curved surface area = πrl (l = slant height)
Sphere: volume = ⁴⁄₃πr³ · surface area = 4πr²
Prism: volume = area of cross-section × length · surface area = sum of all faces
Check which formulas are given in the exam's formulae and tables booklet, and learn the rest.
Worked examples
1. Circle: area and circumference
A circle has radius 7 cm. Find its area and circumference. Use π = 22/7.
Area = πr² = 22/7 × 49 = 154 cm².
Circumference = 2πr = 2 × 22/7 × 7 = 44 cm.
2. Triangle
A triangle has base 12 cm and perpendicular height 9 cm. Find its area.
Area = ½ × 12 × 9 = 54 cm².
3. Compound shape (shaded area)
A rectangle 10 cm by 8 cm has a circle of radius 3 cm cut out of it. Find the shaded area, to one decimal place.
Rectangle: 10 × 8 = 80 cm².
Circle: π × 3² = 9π ≈ 28.27 cm².
Shaded area = 80 − 28.27 ≈ 51.7 cm².
The method is always the same: whole shape minus the part that's not shaded. For more examples, see our area of the shaded region guide.
4. Cylinder
A cylinder has radius 5 cm and height 12 cm. Find its volume in terms of π, then to the nearest cm³.
V = πr²h = π × 25 × 12 = 300π cm³ ≈ 942 cm³.
5. Cone
A cone has radius 6 cm and height 8 cm. Find its volume in terms of π.
V = ⅓πr²h = ⅓ × π × 36 × 8 = 96π cm³.
Its slant height is l = √(6² + 8²) = √100 = 10 cm, so the curved surface area is πrl = π × 6 × 10 = 60π cm².
6. Working backwards
A cylinder holds 1,000 cm³ and has radius 5 cm. How tall is it, to one decimal place?
1,000 = π × 25 × h, so h = 1,000 / (25π) ≈ 12.7 cm.
Units: the easy marks people lose
Length: cm, m
Area: cm², m²
Volume: cm³, m³
Capacity: 1,000 cm³ = 1 litre
Converting area and volume isn't the same as converting length: 1 m = 100 cm, but 1 m² = 10,000 cm² and 1 m³ = 1,000,000 cm³.
Exam tips
Draw and label a sketch for every compound shape.
Write the formula first, then substitute.
Check the instructions for π: "in terms of π", 3.14, 22/7 or the calculator value.
Always give units.
Sense-check answers: a shaded area can't be bigger than the whole shape.
Tips are MMS editorial guidance.
Common mistakes
Using the slant height instead of the perpendicular height. Area and volume need the perpendicular height.
Mixing up radius and diameter. r = d ÷ 2.
Forgetting ⅓ for cones. A cone holds a third of the matching cylinder.
Squaring the wrong number. In πr², only r is squared.
When extra support might help
Support is worth considering when compound shapes are confusing, when formulas aren't sticking, or when a student wants exam-style practice before the Junior Cycle.
A grind can't guarantee a grade, but can build method and confidence. Math Make Smart offers online maths grinds and Junior Cycle support, and you can book a free grind. For the bigger picture, see our Junior Cycle maths guide.
Frequently asked questions
What's the difference between area and perimeter?
Perimeter is the distance around a shape; area is the space inside it.
What is the formula for the volume of a cylinder?
V = πr²h.
How do I find a shaded area?
Find the whole area, then subtract the area that isn't shaded.
How many cm² are in 1 m²?
10,000.