Mensuration Formulas for CAT SSC CGL and Other Exams

Mensuration formulas are frequently featured in exams such as CAT, SSC CGL, and other similar exams. These formulas are a part of geometry and require the aspirant to have knowledge of not only the mensuration formulas but also other theorems and concepts of geometry. However, mensuration questions are usually less difficult compared to other types of geometry questions.

To excel in mensuration questions, aspirants must be well-versed in diverse concepts of mensuration and geometric shapes like triangles, circles, rectangles, squares, cones, cuboids, cubes, cylinders, and spheres. Familiarity with area, perimeter, and volume formulas for these shapes is essential. This article offers advanced Mensuration Formulas for CAT SSC CGL and Other Exams, geometry shortcuts and tricks for effective problem-solving.

All Mensuration Formulas for Triangles:

– Perimeter of a triangle (P) = a + b + c, where a, b, and c are the sides of the triangle
– Semi Perimeter of a triangle (s) = (a + b + c)/2
– Area of triangle = sqrt [ s(s – a)(s – b)(s – c) ] – Area of triangle = r * s, where r is the in-radius of the triangle
– Area of triangle = (abc)/(4R), where R is the circum-radius of the triangle
– Area of triangle = (4/3) * sqrt [ u(u – d)(u – e)(u – f) ], where d, e, and f are medians and u = (d + e + f)/2
– Area of triangle = (1/2) * ab * sin(theta), where a and b are the two known sides and theta is the included angle

Mensuration Formulas for Circles:

Circumference of a circle = 2pi * r, where r is the radius
– Area of a circle = pi * r^2
– Length of an arc = (theta/360) * 2pi * r
– Area of a sector = (theta/360) * pi * r^2
– Area of a segment = (theta/360) * pi * r^2 – (1/2) * r^2 * sin(theta)

Mensuration Formulas for Quadrilaterals:

Area of any Quadrilateral = (1/2) * one diagonal * (h1 + h2)
– Area of any Quadrilateral = (1/2) * d1 * d2 * sin(theta), where d1 and d2 are the diagonals of the quadrilaterals and theta is the angle between them
– Area of any Quadrilateral = sqrt [ (s – a)(s – b)(s – c)(s – d) – abcd * cos^2(alpha) ], where alpha is the average of any pair of opposite angles of the quadrilateral and s = (a + b + c + d)/2
– Perimeter of Rectangle = 2(length + breadth)
– Area of Rectangle = length * breadth
– Perimeter of Square = 4a
– Area of Square = a^2
– Perimeter of Parallelogram = 2(a + b)
– Area of Parallelogram = base * height
– Perimeter of Rhombus = 4a
– Area of Rhombus = (1/2) * d1 * d2, where d1 and d2 are the two diagonals of the Rhombus
– Area of Trapezium = (1/2) * (a + b) * h, where a and b are the parallel sides of the trapezium and h is the perpendicular distance between them

Mensuration Formulas for Polygons:

Area of a regular polygon = (1/2) * apothem * perimeter
– Sum of interior angles = (n – 2) * 180°
– Interior angle = ((n – 2)/n) * 180° for regular polygons
– Exterior angle = (360°/n) for regular polygons

Mensuration Formulas for Solid (3D) Geometry:

Total Surface Area of Cuboid = 2(lw + lh + wh)
– Volume of Cuboid = lwh
– Total Surface Area of Cube = 6a^2
– Volume of Cube = a^3
– Lateral Surface Area of Prism = perimeter of base * height
– Total Surface Area of Prism = 2 * area of base + perimeter of base * height
– Volume of Prism = area of base * height
– Lateral Surface Area of Pyramid = (1/2) * perimeter of base * slant height
– Total Surface Area of Pyramid = area of base + area of base + (1/2) * perimeter of base * slant height
– Volume of Pyramid = (1/3) * area of base * height
– Curved Surface Area of Cylinder = 2pi * rh
– Surface Area of Cylinder = 2pi * r * (r + h)
– Volume of Cylinder = pi * r^2 * h
– Curved Surface Area of Cone = pi * rl, where l is the slant height
– Total Surface Area of Cone = pi * r * (r + l)
– Volume of Cone = (1/3) * pi * r^2 * h
– Total Surface Area of Sphere = 4pi * r^2
– Volume of Sphere = (4/3) * pi * r^3
– Curved Surface Area of Hemisphere = 2pi * r^2
– Total Surface Area of Hemisphere = 3pi * r^2