Study Material — 1 PYQs (2019–2019) · Concept Notes · Shortcuts
RRB Group D Quadrilaterals is a frequently tested subtopic — 1 previous year questions from 2019–2019 papers are included below with concept notes, key rules and shortcut tricks.
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.
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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 Time-Saving Trick:
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.
Common Mistake:
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
3graded MCQs · easy to hard · full solution & trap analysis
A parallelogram has a base of 24 cm and a height of 15 cm. If the height is measured perpendicular to the base, what is the area of the parallelogram?
Practice 2medium
A quadrilateral ABCD has diagonals AC and BD intersecting at point O. If AC = 24 cm, BD = 18 cm, and the diagonals intersect at right angles, find the area of the quadrilateral.
Practice 3hard
A quadrilateral ABCD has diagonals AC and BD intersecting at point O. The diagonals divide the quadrilateral into four triangles. If AC = 20 cm, BD = 24 cm, and the diagonals intersect at right angles, the ratio of the areas of triangles AOB and COD is 4:9. Find the length of AO (in cm).
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