Mensuration (2D Figures) : Formulas & Short Notes
In this article, we have discussed formulas of important 2D figures which are frequently asked. We have compiled important information which are mostly asked in SSC Exams at one place.
# Rectangle
Let d_{1} and d_{2} are diagonals of the given rectangle ABCD.
then, both diagonals are equal but not perpendicular to each other.
Area of rectangle = length x breadth and perimeter = 2(length+breadth)
# Path outside the rectangle
Suppose there is a park having length l and breadth b. There is a road of width x outside of it.
Then, Area of path = 2x (l + b + 2x)
# Path inside the rectangle
Suppose there is a park having length l and breadth b. There is a road of width x inside of it.
Then, Area of path = 2x (l + b – 2x)
# When there is a road along both the length and breadth of the park.
Then, Remaining area of Rectangle (shaded region) = (l–x) (bx)
Area of the path = lx + bx – x^{2}
Area of the path = lx + bx – x^{2}
# Circle: Given a circle of radius ‘r’
We recommend you learn this table as it will save your time in calculating these all.
If radius is ‘r’, then perimeter = 2πr and Area = πr^{2}
Radius

Perimeter (2πr)

Area (πr^{2})

7

44

154

14

88

616

21

133

1386

28

176

2464

35

220

3850

42

264

5544

# Length of Rope
Let ‘d’ is the diameter of pulley and ‘r’ is the radius, then d = 2r. All pulleys are similar.
Let ‘d’ is the diameter of pulley and ‘r’ is the radius, then d = 2r. All pulleys are similar.
Length of rope = 2d + 2pr
Length of rope = 3d + 2pr
Length of rope = 4d + 2pr
Note: Trick to remember these formulas: number of pulleys x diameter + Perimeter of one pulley
#Sector
In this circle, ‘r’ is the radius, θ is the angle made by the arc of length ‘l’
Length of arc
Area of sector
Area of sector when ‘l’ is given

# Segment
Area of minor segment
Area of major segment
# Area of shaded portion
# Inradius and Circumradius of Square:
There is a square of side ‘a’; ‘r’ is the inradius and ‘R’ is the circumradius.
# Triangle:
Let ABC is a triangle and M_{1}, M_{2} and M_{3 }are medians of the given triangle.
Then,
# Inradius of triangle:
Given, ABC is a triangle and a, b and c are the sides of given triangle. Let ‘r’ is the inradius of triangle.
# Circumradius of triangle:
Given, ABC is a triangle and a, b and c are the sides of given triangle. Let ‘R’ is the circumradius of triangle.
# Right angle triangle
Given ‘a’ is the base, ‘b’ is the perpendicular and ‘c’ is the hypotenuse of triangle ABC.
# Equilateral triangle:
Where, h is the height of triangle,
Hence, we can say that height of equilateral triangle is equal to the sum of side perpendicular of the triangle.
# Isosceles triangle
# Regular Polygon
Let, n = no. of sides of regular polygon and a = length of side of regular polygon
# Internal angle of regular polygon =
# Sum of internal angle of regular polygon
# Angle made by centre =
#Area of Regular polygon
or
# External angle of regular polygon
# sum of all external angle = 360º
# sum of all external angle = 360º
# For Regular Hexagon
Circumradius R = a
Inradius

# Cyclic Quadrilateral
# Parallelogram
Let a and b are the sides, h is the height and d_{1} and d_{2} are the diagonals of parallelogram
then,
Area of parallelogram = (i) Base × height
(ii)
(iii)
Imp. Relation
Imp. Note: In rectangle, parallelogram, square and Rhombus diagonals bisect other.
# Rhombus
In Rhombus, diagonals are not equal to each other but they bisect each other at 90 degree.
Area = Base × height = a x h
Or Area
# Trapezium
Case 1: If AD = BC, then DM = CN
# Quadrilateral
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