2D Mensuration: Area and Perimeter

Perimeter vs area

• Perimeter: length of the boundary (units: cm, m).
• Area: surface enclosed (units: cm², m²).

Key formulas

Figure	Area	Perimeter
Rectangle (l, b)	l × b	2(l + b)
Square (a)	a²	4a
Triangle (base b, height h)	½ × b × h	sum of sides
Circle (r)	πr²	2πr

• Equilateral triangle (side a): area = (√3/4)a².
• Diagonal of a square = a√2; of a rectangle = √(l² + b²).

Examples

• Square with area 81 cm² → side 9 → perimeter 36 cm.
• Circle of radius 7 cm (π = 22/7): circumference = 44 cm, area = 154 cm².

Exam tips (RRB NTPC)

1. Check whether the question gives radius or diameter.
2. Use π = 22/7 when the radius is a multiple of 7.

Analogy

Perimeter is the fence around a field; area is the grass inside it. To fence the field you buy wire by the metre; to plant grass you buy turf by the square metre. Two fields can need the same length of fence but hold very different amounts of grass.