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SSC GD Constable Quadrilaterals

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This page covers SSC GD Constable Quadrilaterals with complete concept notes, 12 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Quadrilaterals— Rules & Concept

Core ConceptRead 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.

Key RulesCore 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

Exam PatternsWhat 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.

Worked ExampleSolve 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

ShortcutsUse 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.

Exam TrapsCommon 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

12graded 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

A rectangle has length 20 cm and diagonal 25 cm. What is the breadth of the rectangle?

Practice 3easy

A square has side length 15 cm. What is the length of its diagonal?

Practice 4easy

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

Practice 5easy

A parallelogram has base 18 cm and height 10 cm. What is its area?

Practice 6easy

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

Practice 7medium

A parallelogram has sides of 20 cm and 15 cm. The angle between them is 60°. What is the area of the parallelogram?

Practice 8medium

A square and a rectangle have the same perimeter of 48 cm. The rectangle's length is 14 cm. What is the difference between the area of the square and the area of the rectangle?

Practice 9medium

In a rectangle, the length is 3 cm more than the width. If the perimeter is 54 cm, what is the area of the rectangle?

Practice 10medium

A trapezium has parallel sides of 18 cm and 12 cm, and the perpendicular distance between them is 8 cm. What is its area?

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?

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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