Learn Mensuration for CAT Quantitative Aptitude

Let us begin by reviewing the overall picture of this topic to help us understand the span and depth required to attempt the CAT problems.

The serious aspirants will have to gather the formulae as well as the style of questions that may be framed across various sub-topics in Mensuration.

Mensuration is the evaluation or calculation using suitable formulae without actual measurements of the geometrical concepts such as

(1) length (of a straight line or and of the curve)
(2) area  (of the plane figure or bounded by curves)

From CAT perspective, the problems on length of straight line or a curve are simple and are seldom tested. We, too, will focus on Mensuration beginning with simple polygons like triangles.

Area of Triangles

Δ ABC with the sides:

BC = a; CA = b; AB = ∠A = angle opposite to side a etc.

r = in-radius; R = circum; h = height/ altitude

Area = 1/2 base x altitude

= 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B

, Where r is the circum-radius

= rs where r is the in-radius and semi-perimeter s =

                                                                     also r =

Area of a right angled triangle = half the product of the sides enclosing the right angle

Equilateral Traiangles

       area of an equilateral traiangle = Where 'a' is side.

Isosceles Triangles

Area

In an isosceles right angled traingle

Hypotenuse = where a is the congruent side

Regular Hexagon

Area of a regular hexagon = (i.e 6 time the area of an equilateral triangle)