Geometry and Mensuration Formula Guide for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
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Geometry and mensuration questions come in every SSC maths paper, and the formulas are the only thing you must know. This geometry and mensuration formula guide for SSC gives the area and perimeter of plane shapes, the volume and surface area of solids, the angle formulas of polygons and the Pythagoras triples in tables.
Plane Figures
| Shape | Area | Perimeter or other |
|---|---|---|
| Square (side a) | a² | 4a; diagonal = a√2 |
| Rectangle (l, b) | l × b | 2(l + b); diagonal = √(l² + b²) |
| Triangle | ½ × base × height | Sum of the sides |
| Equilateral triangle (side a) | (√3 / 4) a² | 3a; height = (√3 / 2) a |
| Triangle by Heron | √[s(s − a)(s − b)(s − c)] | s = (a + b + c) / 2 |
| Parallelogram | base × height | 2(a + b) |
| Rhombus | ½ × d₁ × d₂ | 4a |
| Trapezium | ½ (a + b) × h | Sum of the sides |
| Circle (radius r) | πr² | Circumference = 2πr |
Solids
| Solid | Volume | Surface area |
|---|---|---|
| Cube (side a) | a³ | Total 6a²; diagonal = a√3 |
| Cuboid (l, b, h) | l × b × h | Total 2(lb + bh + hl); diagonal = √(l² + b² + h²) |
| Cylinder | πr²h | Curved 2πrh; total 2πr(r + h) |
| Cone | ⅓ πr²h | Curved πrl; total πr(r + l); l = √(r² + h²) |
| Sphere | (4/3) πr³ | 4πr² |
| Hemisphere | (2/3) πr³ | Curved 2πr²; total 3πr² |
Polygons and Angles
- Sum of the interior angles of a polygon of n sides = (n − 2) × 180°.
- Each interior angle of a regular polygon = (n − 2) × 180° / n.
- Sum of the exterior angles of any polygon = 360°.
- Number of diagonals of a polygon = n(n − 3) / 2.
- The angle sum of a triangle is 180°.
Pythagoras and Triples
In a right-angled triangle, (hypotenuse)² = (base)² + (height)². The common triples are 3-4-5, 5-12-13, 8-15-17 and 7-24-25.
Solved Examples
Example 1. Find the area of a circle of radius 7 cm. Use π = 22/7.
(22/7) × 7 × 7 = 154 square cm.
Example 2. Find the volume of a cylinder with radius 7 cm and height 10 cm.
(22/7) × 49 × 10 = 1540 cubic cm.
Example 3. Find each interior angle of a regular pentagon.
(5 − 2) × 180 / 5 = 540 / 5 = 108°.
Quick Tips
- Use π = 22/7 when the radius is a multiple of 7.
- Learn the Pythagoras triples, because they save a lot of time.
- Check the units: square units for the area and cubic units for the volume.
- Write the formula first and then put in the numbers.
Quick Revision Points
- Area of a circle = πr².
- Volume of a cylinder = πr²h.
- Volume of a sphere = (4/3)πr³.
- Sum of the interior angles = (n − 2) × 180°.
- Common triples: 3-4-5, 5-12-13, 8-15-17 and 7-24-25.
Practice Questions With Answers
- Find the area of a circle of radius 7 cm (use 22/7).
Answer: 154 square cm - Find the volume of a cube of side 3 cm.
Answer: 27 cubic cm - Find the diagonal of a rectangle of 3 cm by 4 cm.
Answer: 5 cm - Find the total surface area of a cube of side 2 cm.
Answer: 24 square cm - Find the volume of a cylinder of radius 7 cm and height 10 cm (use 22/7).
Answer: 1540 cubic cm - Find the sum of the interior angles of a hexagon.
Answer: 720° - Find each interior angle of a regular pentagon.
Answer: 108° - Find the area of an equilateral triangle of side 4 cm.
Answer: 4√3 square cm - Find the volume of a sphere of radius 3 cm.
Answer: 36π cubic cm - Find the hypotenuse of a right-angled triangle with sides 5 cm and 12 cm.
Answer: 13 cm
How to Practise This Chapter
Write each formula on a card, with a solved example on the back, and revise the cards every day. Then test yourself with our practice papers and the previous year papers page. See all guides on the Formula Guide page, and also read the Mathematics notes and Quantitative Aptitude notes. The previous guide is Arithmetic and the next guide is Algebra and Trigonometry.
Frequently Asked Questions
What is the area of a circle?
The area of a circle is pi times the radius squared.
What is the volume of a cylinder?
It is pi times the radius squared times the height.
What is the volume of a cone?
It is one-third times pi times the radius squared times the height.
What is the volume of a sphere?
It is four-thirds times pi times the radius cubed.
What is the total surface area of a cube?
It is six times the side squared.
What is the sum of the interior angles of a polygon?
It is (n minus 2) times 180 degrees.
What is the area of an equilateral triangle?
It is root 3 divided by 4, times the side squared.
What are the Pythagoras triples?
The common ones are 3-4-5, 5-12-13, 8-15-17 and 7-24-25.
Which value of pi should I use?
Use 22/7 when the radius is a multiple of 7, and 3.14 otherwise.
Is Mensuration important for SSC exams?
Yes. Several questions come from geometry and mensuration in every SSC maths paper.
How should I revise the formulas?
Write them on cards and solve one example for each shape.
How many questions come from this topic in SSC exams?
Usually three to six questions, but the number changes from exam to exam.
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Arithmetic Formula Guide for SSC Exams
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Algebra and Trigonometry Formula Guide for SSC Exams
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.