What is the Difference Between Parallelogram, Trapezium, and Kite?
The concept of Parallelogram, Trapezium, and Kite plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. These are all special types of quadrilaterals, each with its unique properties about sides, angles, and diagonals. Mastering their differences is essential for scoring well and solving geometry problems quickly in school and competitive exams.
What Is Parallelogram, Trapezium, and Kite?
A parallelogram is a quadrilateral where both pairs of opposite sides are parallel and equal in length. The trapezium (also known as a trapezoid in some countries) is a four-sided shape with only one pair of parallel sides. A kite is a quadrilateral with two pairs of adjacent sides equal in length. You’ll find these concepts applied in geometry, mensuration, and logical reasoning problems.
Properties Comparison Table
| Property | Parallelogram | Trapezium | Kite |
|---|---|---|---|
| Definition | Opposite sides parallel and equal | One pair of sides parallel | Two pairs of adjacent sides equal |
| Equal Sides | Opposite sides | Only in isosceles trapezium | Adjacent sides (two pairs) |
| Equal Angles | Opposite angles | Base angles (isosceles only) | One pair of opposite angles |
| Diagonals | Bisect each other | May not bisect | One diagonal bisects the other at 90° |
| Angle Sum | 360° | 360° | 360° |
| Parallel Sides | 2 pairs | 1 pair | None |
Key Formulas for Parallelogram, Trapezium, and Kite
Parallelogram
Perimeter = 2 × (sum of adjacent sides)
Trapezium
Perimeter = sum of all four sides
Kite
Perimeter = 2 × (sum of distinct side lengths)
How to Identify: Parallelogram, Trapezium, or Kite?
Use these tips during exams or quick revision time:
- If both pairs of sides are parallel, it is a parallelogram.
- If only one pair of opposite sides is parallel, it’s a trapezium.
- If two pairs of sides are equal but the equal ones are adjacent, you have a kite.
Angle Properties and Relationships
Sum of internal angles in any quadrilateral (including parallelogram, trapezium, and kite) is always 360°.
- In a parallelogram, opposite angles are equal, consecutive angles are supplementary (add up to 180°).
- In a kite, one pair of opposite angles are equal (between unequal sides).
- In a trapezium, the sum of angles between each leg and the parallel sides is 180°.
Step-by-Step Illustration: Solved Examples
1. Area of a Parallelogram
Given base = 8 cm, height = 5 cm.
Find the area.
2. Substitute values: 8 × 5 = 40
3. Final Answer: 40 cm²
2. Area of a Trapezium
Given parallel sides: 10 cm and 6 cm, height = 4 cm.
Find the area.
2. Substitute values: ½ × (10 + 6) × 4 = ½ × 16 × 4 = 8 × 4 = 32
3. Final Answer: 32 cm²
3. Perimeter of a Kite
Sides are 7 cm and 9 cm.
Find the perimeter.
2. Substitute values: 2 × (7 + 9) = 2 × 16 = 32
3. Final Answer: 32 cm
Speed Trick or Vedic Shortcut
For parallelogram, trapezium, and kite area questions, quickly check if you know the formula before starting. Repeat the trick: Area of kite is always half the product of diagonals. For trapezium, average the parallel sides and multiply by height. These small techniques can help save time in exams. Vedantu often shares such tips in maths trick lessons and live classes.
Try These Yourself
- Find the area of a parallelogram with base 12 cm and height 7 cm.
- If a kite’s diagonals are 8 cm and 10 cm, what is its area?
- Which of the following is not a quadrilateral: parallelogram, kite, triangle, trapezium?
- Among the given quadrilaterals, which has only one pair of parallel sides?
Frequent Errors and Misunderstandings
- Confusing parallelogram with the kite and trapezium, especially with regards to parallel sides.
- Applying the area formula for kite or parallelogram incorrectly (mixing up diagonals and base/height).
- Assuming all kites have equal diagonals (they only cross at ninety degrees, not always equal length).
Relation to Other Concepts
Understanding parallelogram, trapezium, and kite helps with recognizing all types of quadrilaterals, calculating more complex shapes, and extends to topics like areas of triangles and parallelograms or figures with symmetry, which are key in advanced geometry, physics, and design.
Classroom Tip
A quick way to remember: “A parallelogram has both pairs of opposite sides parallel; a trapezium has only one; a kite has adjacent sides equal.” Vedantu’s teachers use “P-T-K” (Parallel-Two-One, Kite-Adjacent) as a mnemonic device for easy recall during class.
Summary and Exam Tips
- Always check the parallel sides to distinguish between parallelogram and trapezium.
- Don’t mix up base and diagonal formulas when working out areas.
- Use property tables for fast revision before exams.
- For MCQs, remember the unique diagonal rules: parallelogram (bisect each other), kite (one bisects at right angle).
We explored Parallelogram, Trapezium, and Kite—from definitions, key properties, formulas, solved examples, and frequent mistakes. Keep practicing with Vedantu and check out in-depth guides like Properties of Parallelogram to strengthen your understanding and excel in your maths exams!
FAQs on Parallelogram, Trapezium, and Kite Explained: Properties, Formulas, and Key Differences
1. What are the properties of a parallelogram, trapezium, and kite?
A parallelogram has two pairs of parallel sides, opposite sides are equal, and opposite angles are equal. A trapezium (or trapezoid) has only one pair of parallel sides. A kite has two pairs of adjacent equal sides, and its diagonals intersect at right angles.
2. Are trapezium and kite parallelograms?
No. A parallelogram requires two pairs of parallel sides. Trapeziums have only one pair, and kites have no parallel sides (unless it's a special case like a rhombus).
3. What formulas are used to find the area of each shape?
Parallelogram: Area = base × height
Trapezium: Area = ½ × (sum of parallel sides) × height
Kite: Area = ½ × diagonal₁ × diagonal₂
4. How do you distinguish between a kite and a trapezium?
A kite has two pairs of adjacent equal sides, while a trapezium has one pair of parallel sides. Kites have diagonals that intersect at right angles; trapeziums do not necessarily have this property.
5. What is the angle sum property in these quadrilaterals?
The sum of interior angles in any quadrilateral (including parallelograms, trapeziums, and kites) is always 360 degrees.
6. Can a figure be both a kite and a parallelogram at the same time?
Yes, a rhombus is both a kite and a parallelogram. It satisfies the conditions for both shapes: two pairs of equal adjacent sides (kite) and two pairs of parallel sides (parallelogram).
7. Why is the trapezium called a “trapezoid” in some countries?
It's a difference in terminology between British English (trapezium) and American English (trapezoid). Both refer to the same quadrilateral.
8. Do all kites have congruent diagonals?
No. Only a special type of kite, the rhombus, has congruent diagonals. In general, a kite's diagonals are not equal in length.
9. When is a trapezium also a rectangle?
A trapezium becomes a rectangle when it has four right angles and two pairs of parallel sides (meaning it becomes a special case of a parallelogram).
10. Are there real-life objects shaped like kites or trapeziums?
Yes! Kites are obvious examples. Trapeziums can be seen in architectural structures, bridge supports, and some table designs.
11. What is the difference between a parallelogram and a rhombus?
Both are parallelograms, but a rhombus is a special parallelogram where all four sides are equal in length.
12. What are the differences between a square, rectangle, and rhombus?
A square has four equal sides and four right angles. A rectangle has two pairs of equal sides and four right angles. A rhombus has four equal sides but angles are not necessarily right angles (unless it’s a square!).
