Area (Mensuration)

Area of triangles, circles, polygons

117 practice questionsPage updated 5 Apr 2026Review metadata pendingPractice questions

Mensuration is the branch of mathematics that deals with the measurement of geometric figures, including their areas, perimeters, and volumes. It involves calculating the space occupied by 2D shapes (like triangles, rectangles, circles) and understanding the relationships between different measurements. Mensuration problems commonly appear in aptitude tests and require knowledge of standard formulas and their applications.

Key formulas and rules

Rectangle: Area = length x breadth, Perimeter = 2(length + breadth)

Square: Area = side^2, Perimeter = 4 x side

Triangle: Area = x base x height = sqrt[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2 (Heron's formula)

Circle: Area = pir^2, Circumference = 2pir = pid

Parallelogram: Area = base x height, Perimeter = 2(sum of adjacent sides)

Rhombus: Area = x d x d (product of diagonals), Perimeter = 4 x side

Trapezium: Area = x (sum of parallel sides) x height

Sector of Circle: Area = ( /360 deg) x pir^2, Arc length = ( /360 deg) x 2pir

Semicircle: Area = pir^2, Perimeter = pir + 2r = r(pi + 2)

Ring (Annulus): Area = pi(R^2 - r^2) where R = outer radius, r = inner radius

Equilateral Triangle: Area = (sqrt3/4) x side^2, Height = (sqrt3/2) x side

Isosceles Triangle: Area = (b/4) x sqrt(4a^2 - b^2) where a = equal sides, b = base

Key concepts

Area vs. Perimeter

Area measures the region enclosed within a shape (in square units), while perimeter measures the total boundary length (in linear units). For the same perimeter, a circle has the maximum area. Understanding when to use area versus perimeter formulas is crucial - area is needed for coverage problems (painting, carpeting) while perimeter is needed for boundary problems (fencing, framing).

Area (Mensuration)

Key formulas and rules

Key concepts

Area vs. Perimeter

Units and Conversions

Composite Figures

Pathway Problems

Cost Calculation Problems

Ratio of Areas

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Key formulas and rules

Key concepts

Area vs. Perimeter

Units and Conversions

Composite Figures

Pathway Problems

Cost Calculation Problems

Ratio of Areas

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

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