Important Mathematical Formulas Geometry

1. Pythagoras Formula : h2 = p2 + b2 => h = 풑ퟐ + 풃ퟐ p2 = h2 – b2 => p = √풉ퟐ − 풃ퟐ

b2 = h2 – p2 => b = 풉ퟐ − 풑ퟐ 2. Perimeter of a triangle = sum of the length of its three sides

Perimeter of an equilateral triangle = 3 × sides

3. Perimeter of a rectangle = 2(length + breadth)

Length = 퐩퐞퐫퐢퐦퐞퐭퐞퐫ퟐ – breadth

Breadth = 퐩퐞퐫퐢퐦퐞퐭퐞퐫

ퟐ – length

4. Perimeter of a square = 4 × side

Length of side = 퐩퐞퐫퐢퐦퐞퐭퐞퐫ퟒ

5. Perimeter of a rhombus = 4 × side

Length of side = 퐩퐞퐫퐢퐦퐞퐭퐞퐫ퟒ

6. Perimeter of a parallelogram = 2 ×(sum of two adjacent sides)

7. Circumference of a circle = 2훑r

8. Perimeter of a semicircle = r(훑 + 2)

9. Area of a triangle = ퟏퟐ × base × height

10. Area of a rectangle = length × breadth

Length = 퐀퐫퐞퐚

퐁퐫퐞퐚퐝퐭퐡 Breadth=

퐀퐫퐞퐚퐋퐞퐧퐠퐭퐡

11. Area of a square = side × side

Side of a square = √퐀퐫퐞퐚

12. Area of a parallelogram = Base × Height

13. Area of a rhombus = ퟏퟐ × d1 × d2 [where, d1 and d2 are two diagonals]

14. Area of a trapezium = ퟏퟐ × (a + b) × h [where, 'a' and 'b' are two parallel

sides and 'h' is height]

15. Area of a circle = 훑r2

16. Lateral Surface Area of a cuboid = 2 × (l + b) × h

Total Surface Area of a cuboid = 2 × (lb + bh + lh)

Diagonal of a cuboid = √퐥ퟐ + 퐛ퟐ + 퐡ퟐ

17. Lateral Surface Area of a cube = 4 × l2

Total Surface Area of a cube = 6 × l2

Diagonal of a cube = l√ퟑ

18. Curved Surface Area of a solid cylinder = 2훑퐫퐡

Total Surface Area of a solid cylinder = 2훑r2 +2훑퐫퐡

= 2훑r (r + h)

Curved Surface Area of a hollow cylinder = 2훑퐑퐡 + 2훑퐫퐡 = 2훑퐡(R + r)

Surface Area of a hollow cylinder = 2훑퐫퐡 + 2훑퐑퐡 + 2(훑R2 – 훑r2)

Area of the ring = 훑R2 – 훑r2 = 훑(R2 – r2)

Thickness of the ring = R – r

19. Curved Surface Area of a cone = 훑퐫퐥 [where, l = slant height]

Total Surface Area of a cone = 훑r2 + 훑퐫퐥 = 훑r (r + l)

20. Surface Area of a sphere = 4훑r2

Surface Area of a hemisphere = 3훑r2

21. Surface Area of a prism = 2 × area of base + perimeter of base × height

22. Surface Area of any pyramid = area of base + area of each of lateral faces

23. Surface Area of regular pyramid = area of base + ퟏퟐ × ps

Where, p = perimeter of the base

s = slant height

24. Surface Area of square pyramid = b2 + 2bs

[Where, b = length of the base, s = slant height]