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Agniveer Army CEE Quadrilaterals

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This page covers Agniveer Army CEE Quadrilaterals with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.

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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

8graded MCQs · easy to hard · full solution & trap analysis

All MCQs →

Practice 1easy

A parallelogram has a base of 12 cm and a height of 8 cm. What is its area?

Practice 2easy

The diagonals of a rhombus are 10 cm and 24 cm. Find its area.

Practice 3easy

In a trapezium, the parallel sides are 6 cm and 14 cm, and the height is 5 cm. What is its area?

Practice 4medium

The diagonals of a rhombus are 12 cm and 16 cm. What is the area of the rhombus?

Practice 5medium

In a parallelogram, one angle is 65°. What is the measure of an adjacent angle?

Practice 6medium

A trapezium has parallel sides of lengths 10 cm and 14 cm, with a height of 6 cm. Find its area.

Practice 7medium

In a rectangle, the length is 18 cm and the perimeter is 56 cm. What is the breadth?

Practice 8hard

A quadrilateral ABCD has angles in the ratio 2:3:4:6. If the smallest angle is 40°, what is the measure of the largest angle?

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 & Circumference Cylinder, Cone, Sphere→

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