Trapezium Formulas, Concepts, Strategies, Short Tricks, and Tips

Published on 12 August 2025 by

The Trapezium is a quadrilateral with exactly one pair of parallel sides. It is a frequently tested geometry topic in SSC, Banking, and Railway exams. In this blog we have provided all the details from the definition, key properties, formulas, tricks, solved questions, and more.

What Is Trapezium in Quantitative Aptitude?

Let’s begin by understanding the basic definition and properties of a trapezium and why it is an important topic in quantitative aptitude exams.

A Trapezium (or trapezoid) is a quadrilateral where only one pair of opposite sides are parallel. The parallel sides are called the bases, and the other two are the legs.

Why it appears in exams:

  • Tests knowledge of quadrilaterals and mensuration formulas.
  • Requires application of area and perimeter formulas with height and bases.

Skills required:

  • Understanding parallel sides and height
  • Application of area formula
  • Visualization of shape properties
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Why Is Trapezium Important in Competitive Exams?

Trapezium questions appear regularly in competitive exams due to their moderate difficulty and applicability in mensuration problems.

ExamNo. of QuestionsDifficulty
SSC CGL / CHSL1–2Moderate
IBPS PO / SBI PO1–2Moderate
RRB NTPC / Group D1Easy
State PSC / Police1–2Moderate

Trapezium Quantitative Aptitude Short Notes

This section summarizes the key concepts and terminology related to trapeziums in a concise table for quick reference.

TermDetails
Parallel sides (bases)Only one pair of parallel sides
LegsNon-parallel sides
Height (h)Perpendicular distance between parallel sides
Interior anglesSum is always 360°
Area12×(a+b)×h\frac{1}{2} \times (a + b) \times h21​×(a+b)×h
PerimeterSum of all four sides

Quick Revision Summary

Here’s a quick summary of the essential formulas and facts about trapeziums.

ConceptExplanation
Number of parallel sidesExactly one pair
BasesParallel sides
HeightPerpendicular distance between bases
Area formula12×(a+b)×h\frac{1}{2} \times (a + b) \times h21​×(a+b)×h
Perimeter formulaSum of all sides
Sum of interior angles360°

What Are the Types of Trapezium Questions in Quantitative Aptitude?

Trapezium problems can appear in various forms in exams. Understanding the common question types will help you prepare effectively.

  • Direct formula application: Find area or perimeter given bases and height.
  • Missing side problems: Calculate missing leg using perimeter or Pythagoras theorem (if right trapezium).
  • Mixed problems: Combined with other mensuration topics or coordinate geometry.
  • Angle-based problems: Using properties of trapezium angles.
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Trapezium Formulas for Quantitative Aptitude

In this section, we list all the important formulas related to trapeziums that will help you solve problems faster.

Trapezium Tricks for SSC CGL and Other Exams

These quick tips will help you solve trapezium questions more efficiently in competitive exams.

  1. Always identify which sides are parallel to correctly apply the area formula.
  2. Use the Pythagoras theorem for right trapezium to find missing sides or height.
  3. Remember the sum of interior angles is 360°, helpful in angle-based problems.
  4. Convert complex trapeziums into simpler shapes if possible.
  5. Check units carefully when calculating area and perimeter.

Solved Trapezium Questions from 2024–25 Exams

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Common Mistakes to Avoid while Solving Trapezium Questions

Avoid these common mistakes to score better in trapezium questions:

  • Mixing up legs and bases for area calculation.
  • Forgetting to use the perpendicular height, not the slant height.
  • Incorrectly assuming non-parallel sides are equal.
  • Ignoring units during calculation.
  • Confusing trapezium with parallelogram.

FAQs

Q1. What is the height of trapezium?

The perpendicular distance between the parallel sides.

Q2. Can trapezium be a parallelogram?

No, because a parallelogram has two pairs of parallel sides.

Q3. Are trapeziums cyclic quadrilaterals?

Some trapeziums can be cyclic if the sum of opposite angles is 180°.

Q4. What is the difference between trapezium and trapezoid?

Depends on country usage; often used interchangeably.

Q5. Are trapezium questions asked in SBI PO?

Yes, often in mensuration or DI.