Area and Perimeter — 2D Mensuration

Two-dimensional mensuration is the friendliest scoring block in this chapter because every question reduces to plugging numbers into a known formula. In SBI Clerk Prelims it usually appears as a direct area or perimeter question, or hidden inside a data-interpretation or ratio problem. The rule is simple: memorise the handful of formulas below cold, and the arithmetic that follows is pure substitution. No proofs, no derivations — just fast, accurate plugging in of the given sides or radius.

The Five Shapes You Must Know Cold

SBI Clerk restricts itself to five everyday shapes: square, rectangle, triangle, circle and parallelogram. Each has an area formula and a perimeter or circumference formula, and none of them is complicated. The single most common mistake is mixing up area with perimeter under time pressure, so anchor the units in your head — area is always in square units, perimeter in plain units. Learn the table below so well that you write the formula before you finish reading the question.

Square, Rectangle and Parallelogram

For a square, everything follows from the side: area is side squared and perimeter is four times the side, and the diagonal is the side times root two. A rectangle needs both length and breadth — area is their product and perimeter is twice their sum. A parallelogram behaves like a rectangle for area, using base times perpendicular height, not the slanted side. Confusing the slant side with the height is the classic parallelogram trap, so always use the vertical height given in the figure.

Triangle and Circle Essentials

For a triangle the standard area is half base times height, but when only the three sides are known, use Heron's formula. For an equilateral triangle a direct shortcut avoids height altogether. The circle rests entirely on the radius: area is pi r squared and circumference is two pi r. Take pi as 22/7 when the radius is a multiple of 7 and as 3.14 otherwise — choosing the right form of pi is itself a small speed trick.

Heron: s = (a+b+c)/2, Area = √[s(s−a)(s−b)(s−c)] Equilateral area = (√3/4) × side²

Solved Examples

Example 1: A rectangle is 14 m long and 9 m wide. Area = 14 × 9 = 126 m² and perimeter = 2 × (14 + 9) = 46 m. Example 2: A circle has radius 7 cm. Take π = 22/7, so area = 22/7 × 49 = 154 cm² and circumference = 2 × 22/7 × 7 = 44 cm — no decimals needed because 7 cancels cleanly.

✗ Using the slanted side of a parallelogram as its height  |  ✓ Using the perpendicular height with base for area

Which Version of the Question Is Asked

SBI Clerk rarely asks a bare formula; it dresses the shape in a sentence. A question about fencing a field or the length of wire around a plot is a perimeter question; a question about tiling, painting or the cost of grassing is an area question, priced per square unit. When a problem gives you the area and asks for a side, simply reverse the formula. And when it changes one dimension — doubling the radius or increasing the side by a percentage — remember that area scales with the square of the change, so doubling the side quadruples the area. Spotting whether the answer wants a boundary length or a covered surface, and knowing how area responds to a change in dimension, settles almost every 2D question before you compute a single number.