How many Quadrilaterals & Polygons questions come in CAT Quant?

About 1.3 questions in a 22-question Quant section, worth roughly 4 marks. Quadrilaterals & Polygons appeared in 21 of the 24 CAT papers from 2017 to 2025, 32 questions in all, which ranks it 6 of 25 Quant chapters.

Are Quadrilaterals & Polygons questions in CAT MCQ or TITA?

25% of the Quadrilaterals & Polygons questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.

What types of Quadrilaterals & Polygons questions does CAT ask?

CAT keeps returning to 7 question shapes in Quadrilaterals & Polygons: Inside a regular hexagon or octagon; A rectangle under a constraint; A trapezium; A rhombus, which means its diagonals; Areas split inside a rectangle or square; Regular polygon angle arithmetic; A parallelogram.

Quadrilaterals & Polygons for CAT: Formulas, Weightage & Question Types

Regular hexagons and octagons, rhombus diagonals, trapeziums and polygon angles.

Quadrilaterals & Polygons formula sheet

Everything CAT needs from Quadrilaterals & Polygons, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place. $a$ is a side, $h$ a height, $d_1$ and $d_2$ the diagonals.

Rectangle and square


Rectangle, area	$lb$
Rectangle, perimeter	$2(l+b)$
Rectangle, diagonal	$\sqrt{l^2+b^2}$ — the square root is not optional
Square, area	$a^2$
Square, diagonal	$a\sqrt{2}$
Rectangle in a circle	the diagonal is the diameter, so $l^2+b^2 = 4R^2$

Parallelogram


Area	$\text{base} \times h = ab\sin\theta$
Height versus side	$h \le$ the slant side, always — this is a hidden inequality
Diagonals	they bisect each other
Diagonal identity	$d_1^2 + d_2^2 = 2(a^2+b^2)$

Rhombus — four equal sides


Diagonals	perpendicular bisectors of each other
Area	$\dfrac{1}{2}d_1d_2$
Side and diagonals	$d_1^2 + d_2^2 = 4a^2$
Area, from the angle	$a^2\sin\theta$
Inradius	$r = \dfrac{\text{area}}{2a}$

Trapezium


Area	$\dfrac{1}{2}(\text{sum of the parallel sides}) \times h$
A leg perpendicular to both parallels	that leg is the height
Legs extended to a point	the two triangles are similar, in the ratio of the parallel sides

Circles in and around


A circle fits inside a quadrilateral exactly when	$AB + CD = BC + AD$
Then	$\text{area} = r \times \text{semiperimeter}$
A circle fits around it exactly when	opposite angles add to $180^\circ$

Any regular polygon, $n$ sides


Exterior angle	$\dfrac{360^\circ}{n}$
Interior angle	$\dfrac{180^\circ(n-2)}{n}$
The quick one	interior $+$ exterior $= 180^\circ$
Sum of interior angles	$180^\circ(n-2)$
Number of diagonals	$\dfrac{n(n-3)}{2}$

Regular hexagon, side $a$ — six equilateral triangles


Area	$\dfrac{3\sqrt{3}}{2}a^2$
Short diagonal, spanning two sides	$a\sqrt{3}$
Long diagonal, straight across	$2a$
Distance from centre to a vertex	$a$

Regular octagon, side $a$


Area	$2(1+\sqrt{2})a^2$
Diagonal spanning two sides	$a\sqrt{2+\sqrt{2}}$

Limits


Each side of a quadrilateral	is less than the sum of the other three
Fixed perimeter	the square has the largest area
Fixed area	the square has the smallest perimeter

The 7 Quadrilaterals & Polygons question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine. Beyond these, CAT has asked 1 rarer one-off shape here.

01
Inside a regular hexagon or octagon
02
A rectangle under a constraint
03
A trapezium
04
A rhombus, which means its diagonals
05
Areas split inside a rectangle or square
06
Regular polygon angle arithmetic
07
A parallelogram

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Quadrilaterals & Polygons in CAT: quick answers

How many Quadrilaterals & Polygons questions come in CAT Quant?: About 1.3 questions in a 22-question Quant section, worth roughly 4 marks. Quadrilaterals & Polygons appeared in 21 of the 24 CAT papers from 2017 to 2025, 32 questions in all, which ranks it 6 of 25 Quant chapters.
Are Quadrilaterals & Polygons questions in CAT MCQ or TITA?: 25% of the Quadrilaterals & Polygons questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Quadrilaterals & Polygons questions does CAT ask?: CAT keeps returning to 7 question shapes in Quadrilaterals & Polygons: Inside a regular hexagon or octagon; A rectangle under a constraint; A trapezium; A rhombus, which means its diagonals; Areas split inside a rectangle or square; Regular polygon angle arithmetic; A parallelogram.

Quadrilaterals & Polygons for CAT: Formulas, Weightage & Question Types

Quadrilaterals & Polygons formula sheet

The 7 Quadrilaterals & Polygons question types CAT repeats

Is Quadrilaterals & Polygons costing you marks?

Quadrilaterals & Polygons in CAT: quick answers

More Geometry for CAT