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RRB NTPC Quadrilaterals

Study Material — 11 PYQs (2019–2019) · Concept Notes · Shortcuts

RRB NTPC Quadrilaterals is a frequently tested subtopic — 11 previous year questions from 2019–2019 papers are included below with concept notes, key rules and shortcut tricks.

11 PYQs
2019–2019
20 Practice
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8 Key Points
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Previous Year Questions

RRB NTPC Quadrilaterals — Past Exam Questions

11 questions from actual RRB NTPC papers · all shown free · click option to reveal solution

Exam Q 12019Previous Year Pattern

A trapezium has parallel sides of 12 cm and 18 cm, and a height of 8 cm. What is its area?

Exam Q 22019Previous Year Pattern

A rectangle has a length of 24 cm and a breadth of 16 cm. What is the perimeter of the rectangle?

Exam Q 32019Previous Year Pattern

The area of a square is 144 cm². What is the length of its diagonal?

Exam Q 42019Previous Year Pattern

A parallelogram has a base of 20 cm and a height of 15 cm. What is its area?

Exam Q 52019Previous Year Pattern

A rhombus has diagonals of length 18 cm and 24 cm. What is its area?

Exam Q 62019Previous Year Pattern

The perimeter of a rhombus is 80 cm. What is the length of each side of the rhombus?

Exam Q 72019Previous Year Pattern

In a rectangle, the length is 5 cm more than the width. If the perimeter is 50 cm, find the area of the rectangle.

Exam Q 82019Previous Year Pattern

A rhombus has diagonals of length 16 cm and 12 cm. What is the side length of the rhombus?

Exam Q 92019Previous Year Pattern

A parallelogram has adjacent sides of 12 cm and 8 cm. If the angle between them is 60°, find the area of the parallelogram.

Exam Q 102019Previous Year Pattern

In a trapezium ABCD with AB ∥ CD, AB = 28 cm, CD = 12 cm, and height = 8 cm. The diagonals AC and BD intersect at point O. Find the ratio of the areas of triangles AOB and COD.

Exam Q 112019Previous Year Pattern

A rectangle ABCD has length 20 cm and width 12 cm. A line segment is drawn from vertex A to a point E on side CD such that CE = 5 cm. Find the area of triangle ACE (in cm²).

Concept Notes

Quadrilaterals— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

A quadrilateral is a closed figure with four sides and four angles. The sum of all interior angles in any quadrilateral is always 360°. This is the most fundamental property you must remember.

There are several types of quadrilaterals: parallelogram, rectangle, square, rhombus, trapezium, and kite. Each has unique properties that SSC CGL tests regularly.

2.Key Rules

Core rules you must know cold
Rectangle

All angles are 90°. Diagonals are equal and bisect each other

Square

All sides equal, all angles 90°. Diagonals are equal, perpendicular, and bisect each other

Rhombus

All sides equal. Diagonals are perpendicular and bisect each other

Trapezium

One pair of opposite sides is parallel. Kite: Two pairs of adjacent sides are equal. One diagonal bisects the other at right angles

Area Formulas

Parallelogram: Base × Height Rectangle: Length × Breadth Square: Side² Rhombus: (1/2) × d1 × d2 (where d1, d2 are diagonals) Trapezium: (1/2) × (sum of parallel sides) × height Kite: (1/2) × d1 × d2

3.Exam Patterns

What examiners ask — read before attempting PYQs
Common question types include

finding area when diagonals are given, calculating perimeter from given conditions, property-based questions, and coordinate geometry problems involving quadrilaterals

Powerful Shortcut - Diagonal Rule

For any quadrilateral with perpendicular diagonals, Area = (1/2) × d1 × d2. This works for rhombus, kite, and square. This single formula can solve multiple question types quickly.

4.Worked Example

Solve this step-by-step before moving on
1
Step 1

Find Area Area = (1/2) × d1 × d2 Area = (1/2) × 16 × 12 = 96 cm²

2
Step 2

Find Side Length Diagonals of rhombus bisect at right angles. Half diagonals: 8 cm and 6 cm Using Pythagoras: Side = √(8² + 6²) = √(64 + 36) = √100 = 10 cm

3
Step 3

Find Perimeter Perimeter = 4 × side = 4 × 10 = 40 cm Another

5.Shortcuts

Use these to save 30–60 seconds per question

When a quadrilateral's vertices are given in coordinate geometry, use the shoelace formula: Area = (1/2)|x1(y2-y4) + x2(y3-y1) + x3(y4-y2) + x4(y1-y3)|. This eliminates the need for multiple calculations.

6.Exam Traps

Common mistakes students make — avoid these

Students often confuse rhombus and square properties. Remember: Square has all properties of rhombus PLUS all angles are 90°. Rhombus doesn't necessarily have 90° angles.

Also, many forget that in trapezium area formula, height is the perpendicular distance between parallel sides, not the slant side length.

Key Points to Remember

  • Sum of interior angles in any quadrilateral = 360°
  • Parallelogram: Opposite sides parallel and equal, diagonals bisect each other
  • Rectangle: All angles 90°, diagonals equal and bisect each other
  • Square: All sides equal, all angles 90°, diagonals equal and perpendicular
  • Rhombus: All sides equal, diagonals perpendicular and bisect each other
  • For perpendicular diagonals: Area = (1/2) × d1 × d2
  • Trapezium area = (1/2) × (sum of parallel sides) × height
  • Kite has two pairs of adjacent sides equal, one diagonal bisects other perpendicularly

Exam-Specific Tips

  • Sum of all interior angles in any quadrilateral is exactly 360°
  • Rhombus area formula: (1/2) × d1 × d2 where d1, d2 are diagonals
  • Square is the only quadrilateral that is both rectangle and rhombus
  • In parallelogram, opposite angles are equal and adjacent angles are supplementary
  • Trapezium has exactly one pair of parallel sides
  • Rectangle diagonals are always equal in length
  • Kite has exactly two pairs of adjacent sides equal
  • In any parallelogram, diagonals bisect each other but are not necessarily equal
Practice MCQs

Quadrilaterals — Practice Questions

20graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A rectangle has length 24 cm and breadth 16 cm. What is the perimeter of the rectangle?

Practice 2easy

The area of a square is 144 cm². What is the length of its diagonal?

Practice 3easy

A trapezium has parallel sides of 10 cm and 14 cm, and a height of 8 cm. What is its area?

Practice 4easy

A quadrilateral has angles of 85°, 95°, and 100°. What is the measure of the fourth angle?

Practice 5easy

A rhombus has diagonals of length 12 cm and 16 cm. What is its area?

Practice 6easy

A rectangle has a length of 24 cm and a breadth of 16 cm. What is the perimeter of the rectangle?

Practice 7easy

The diagonals of a rhombus are 12 cm and 16 cm. Find the area of the rhombus.

Practice 8easy

A trapezium has parallel sides of 10 cm and 14 cm, and a height of 8 cm. Find its area.

Practice 9easy

A parallelogram has a base of 20 cm and a height of 15 cm. What is its area?

Practice 10medium

A square has a side length of 10 cm. If each side is increased by 40%, what is the percentage increase in the area of the square?

Practice 11medium

A rhombus has diagonals of length 16 cm and 12 cm. What is the perimeter of the rhombus?

Practice 12medium

A parallelogram has a base of 24 cm and a height of 15 cm. If the base is increased by 25% and the height is decreased by 20%, what is the percentage change in the area of the parallelogram?

Practice 13hard

In a parallelogram ABCD, the sides AB and AD have lengths 13 cm and 14 cm respectively. The diagonal AC has length 15 cm. If the perpendicular distance from B to the line AC is h cm, then h is closest to which value?

Practice 14hard

In a cyclic quadrilateral PQRS, the diagonals PR and QS intersect at point O. If PO = 8 cm, OR = 6 cm, QO = 12 cm, and OS = x cm, then the perimeter of quadrilateral PQRS is closest to which value? (Given: PQ = 10 cm, RS = 7.5 cm)

Practice 15hard

A rhombus has diagonals of length 30 cm and 16 cm. A circle is inscribed in this rhombus such that it touches all four sides. What is the radius of the inscribed circle?

Practice 16hard

A trapezium ABCD has parallel sides AB and CD of lengths 24 cm and 16 cm respectively. The perpendicular distance between these parallel sides is 15 cm. If a line parallel to both AB and CD divides the trapezium into two smaller trapeziums of equal area, at what perpendicular distance from AB does this dividing line lie?

Practice 17hard

In a trapezium ABCD with AB ∥ CD, the non-parallel sides AD and BC are extended to meet at point P. If AB = 8 cm, CD = 12 cm, and the distance from P to AB is 20 cm, what is the distance from P to CD?

Practice 18hard

A rhombus ABCD has diagonals of lengths 16 cm and 12 cm. A circle is inscribed in this rhombus such that it touches all four sides. If the radius of this inscribed circle is r cm, then the area of the region inside the rhombus but outside the circle is closest to which value?

Practice 19hard

In a cyclic quadrilateral PQRS, the diagonals PR and QS intersect at point O. If PO = 8 cm, OR = 6 cm, QO = 12 cm, and OS = x cm, find the value of x using the property of intersecting chords.

Practice 20hard

A quadrilateral ABCD is inscribed in a circle with sides AB = 5 cm, BC = 6 cm, CD = 7 cm, and DA = 8 cm. Using Brahmagupta's formula, find the area of this cyclic quadrilateral. (Take √840 ≈ 29)

60-Second Revision — Quadrilaterals

  • Remember: All quadrilateral interior angles sum to 360°
  • Formula: Area with perpendicular diagonals = (1/2) × d1 × d2
  • Trap: Square is both rectangle and rhombus, but rhombus is not always rectangle
  • Quick check: Parallelogram opposite sides are parallel AND equal
  • Memory aid: Rectangle = right angles, Rhombus = equal sides
  • Formula: Trapezium area = (1/2) × (parallel sides sum) × height
  • Property: Only square has equal diagonals that are also perpendicular
←Circles — Area & CircumferenceCylinder, Cone, Sphere→
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