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]