Quadrilaterals and Polygons Formula Guide for SSC
Rahul Kumar
SSC Exam Expert & Content Editor
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PDF Notes: Quadrilaterals and Polygons Formula Guide for SSC
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This formula guide gives all the formulas for polygons and quadrilaterals that SSC geometry and mensuration questions use.
Polygons
| Quantity | Formula |
|---|---|
| Sum of interior angles of an n-sided polygon | (n − 2) × 180° |
| Each interior angle of a regular polygon | (n − 2) × 180° / n |
| Sum of exterior angles | 360° |
| Each exterior angle of a regular polygon | 360° / n |
| Number of diagonals | n(n − 3)/2 |
Areas of Quadrilaterals
| Shape | Area | Other facts |
|---|---|---|
| Rectangle | l × b | Diagonal = √(l² + b²) |
| Square | a² | Diagonal = a√2 |
| Parallelogram | base × height | Opposite sides equal |
| Rhombus | ½ × d1 × d2 | Diagonals bisect at 90° |
| Trapezium | ½ × (a + b) × h | a and b are parallel sides |
| Kite | ½ × d1 × d2 | Diagonals perpendicular |
Properties
- Sum of the angles of a quadrilateral is 360°.
- Diagonals of a rectangle are equal and of a square are equal and perpendicular.
- Diagonals of a parallelogram bisect each other.
- A cyclic quadrilateral has opposite angles adding to 180°.
Quick Tips
- Each exterior angle × number of sides = 360°.
- Use diagonals for rhombus and kite areas.
- A square is also a rhombus and a rectangle.
- Cyclic quadrilateral: opposite angles are supplementary.
Quick Revision Points
- Interior angle sum = (n − 2) × 180°.
- Exterior angle sum = 360°.
- Diagonals = n(n − 3)/2.
- Rhombus area = ½ d1 d2.
- Trapezium area = ½(a + b)h.
- Square diagonal = a√2.
Practice Questions With Answers
- Find the sum of the interior angles of a hexagon.
Answer: 720° - Find each interior angle of a regular octagon.
Answer: 135° - Find each exterior angle of a regular pentagon.
Answer: 72° - How many diagonals does a decagon have?
Answer: 35 - Find the area of a rhombus with diagonals 10 cm and 24 cm.
Answer: 120 cm² - Find the area of a trapezium with parallel sides 8 cm and 12 cm and height 5 cm.
Answer: 50 cm² - Find the diagonal of a square with side 6 cm.
Answer: 6√2 cm - How many sides does a regular polygon have if each exterior angle is 30°?
Answer: 12
How to Practise This Chapter
Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Formula Guide notes page.
Frequently Asked Questions
What is the sum of the interior angles of a quadrilateral?
360°.
What is the sum of exterior angles of any polygon?
360°.
How many diagonals are there in a polygon of n sides?
n(n − 3)/2.
What is the area of a rhombus?
Half the product of its diagonals.
What is the area of a trapezium?
Half the sum of the parallel sides times the height.
What is a cyclic quadrilateral?
One whose vertices lie on a circle.
What is a regular polygon?
A polygon with equal sides and equal angles.
What is the diagonal of a square?
Side × √2.
Do the diagonals of a rhombus meet at right angles?
Yes.
How to use this guide?
Memorise the table and solve one problem per formula.
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Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.