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Quantitative Aptitude›Ch 4: Algebra, Geometry & Mensuration›Mensuration 2D: Area & Perimeter
Master 2D formulas, perimeter shortcuts, and area traps for competitive exams.
Perimeter is the total boundary length measured in linear units, while area is the enclosed space measured in square units. Always verify that all dimensions are converted into the exact same unit before applying any formula.
Quick Memory Hooks
| Shape | Perimeter | Area |
|---|---|---|
| Square (side a) | 4a | a² |
| Rectangle (l, b) | 2(l + b) | l × b |
| Circle (radius r) | 2πr | πr² |
| Equilateral Triangle | 3a | (√3/4)a² |
Trapezium
(Parallel sides)
Parallel sides
Area = 0.5 × sum of parallel sides × height.
Rhombus
(Equal sides diagonals)
Equal sides diagonals
Area = half product of diagonals.
Sector
(Pie slice circle)
Pie slice circle
Area = (θ/360) × πr².
Rectangle
(Opposite sides equal)
Opposite sides equal
Diagonal = √(l² + b²).
Adding cm and meters directlyConvert both to same unit first
Examiners love mixing units in perimeter problems to trap careless aspirants.
Confusing perimeter with areaCheck units (m vs m²)
Perimeter is linear (m), area is square (m²). Never equate or add them.
Using diameter instead of radiusAlways divide diameter by 2
For circles and sectors, questions often provide diameter; always use radius r.
Q1.Find the area of a rhombus whose diagonals are 10 cm and 24 cm.
Q2.What is the circumference of a circle with radius 14 cm? (Use π = 22/7)