Basic Mensuration Questions with Solutions

Basic mensuration deals with the perimeter and area of two-dimensional shapes: squares, rectangles, triangles, parallelograms, rhombuses, trapeziums, circles, sectors and rings. Exam questions test direct use of formulas, the effect of changing dimensions (for example, what happens to the area of a circle when its radius increases by 10%), paths running inside or outside a rectangular field, and the cost of fencing, flooring or painting. Knowing the formulas thoroughly is essential, and ratio reasoning makes questions on changing dimensions quick to solve. Remember that when every length is multiplied by k, the area is multiplied by k^2. Heron's formula for a triangle's area from its three sides and the area of an equilateral triangle, (sqrt 3 / 4) a^2, are worth memorising. Three-dimensional solids are covered separately on the Volume & Surface Area page. Practise the mensuration questions below on area and perimeter, each with a step-by-step solution.