CAT 2025 Lesson : Quadrilaterals - Concepts & Cheatsheet

Note: The video for this module contains a summary of all the concepts covered in this lesson. The video would serve as a good revision. Please watch this video in intervals of a few weeks so that you do not forget the concepts. Below is a cheatsheet that includes all the formulae but not necessarily the concepts covered in the video.

6. Cheatsheet

1) Sum of interior angles of an

n-

sided polygon

= ( n - 2 ) \times 180^{\mathrm{o}}

2) Sum of exterior angles of an

n-

sided polygon

= 360^{\mathrm{o}}

3) Number of diagonals in an

n-

sided polygon

= \dfrac{n (n - 3)}{2}

4) In a concave polygon, at least one angle measures more than

180^{\mathrm{o}}

, whereas all angles measure less than

180^{\mathrm{o}}

in a convex polygon.

5) In regular polygons, Each Interior Angle

= \dfrac{( n - 2 ) \times 180^{\mathrm{o}} }{n}

; Each Exterior Angle

= \dfrac{360^{\mathrm{o}}}{n}

6) Area of

n-

sided regular polygon

= n \times \dfrac{1}{2} \times a \times h = \dfrac{1}{2}nah

7) The following are select properties/formulae for certain quadrilaterals.

(Refer \ the \ lesson \ for \ full \ list)

Type	Perimeter	Area	Properties
Quadrilateral	Sum of sides	$\dfrac{1}{2} \times d \times ( h_1 + h_2 )$	Sum of the interior angles of a quadrilateral equals $360^{\mathrm{o}}$
Parallelogram	2 $(a + b)$	$bh = ab sin\theta$	1) Opposite sides are equal, Opposite angles are equal 2) Sum of adjacent angles is $180^{\mathrm{o}}$ 3) Diagonals bisect each other 4) Sum of squares of diagonals = Sum of squares of sides
Rhombus	4 $a$	$bh = \dfrac{1}{2}d_1d_2$	All the properties of parallelogram and 1) All sides are equal 2) Diagonals bisect each other at $90^{\mathrm{o}}$ 3) Circle can be inscribed
Rectangle	2 $(l + b)$	$lb$	All the properties of parallelogram and 1) All angles are equal and $90^{\mathrm{o}}$ 2) Diagonals are equal and bisect each other 3) Circle can be circumscribed
Square	4 $a$	$a^2$	All the properties of Rectangle & Rhombus
Trapezium	Sum of sides	$\dfrac{1}{2} h ( b_1 + b_2 )$	1) The triangles formed by the Diagonals along parallel sides of a trapezium are similar triangles 2) Diagonals divide each other in the same proportion
Kite	2 $(a + b)$	$ab sin\theta= \dfrac{1}{2}d_1d_2$	1) 2 pairs of adjacent sides are equal 2) Diagonals intersect at $90^{\mathrm{o}}$

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