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<strong>Geometry</strong><br />
Important <strong>Mathematical</strong> <strong>Formulas</strong><br />
1. Pythagoras Formula : h 2 = p 2 + b 2 => h = 풑 ퟐ + 풃 ퟐ<br />
p 2 = h 2 – b 2 => p = √풉 ퟐ − 풃 ퟐ<br />
b 2 = h 2 – p 2 => b = 풉 ퟐ − 풑 ퟐ<br />
2. Perimeter of a triangle = sum of the length of its three sides<br />
Perimeter of an equilateral triangle = 3 × sides<br />
3. Perimeter of a rectangle = 2(length + breadth)<br />
Length = 퐩퐞퐫퐢퐦퐞퐭퐞퐫<br />
ퟐ<br />
Breadth = 퐩퐞퐫퐢퐦퐞퐭퐞퐫<br />
ퟐ<br />
4. Perimeter of a square = 4 × side<br />
Length of side = 퐩퐞퐫퐢퐦퐞퐭퐞퐫<br />
ퟒ<br />
5. Perimeter of a rhombus = 4 × side<br />
– breadth<br />
– length<br />
Length of side = 퐩퐞퐫퐢퐦퐞퐭퐞퐫<br />
ퟒ<br />
6. Perimeter of a parallelogram = 2 ×(sum of two adjacent sides)<br />
7. Circumference of a circle = 2훑r<br />
8. Perimeter of a semicircle = r(훑 + 2)<br />
9. Area of a triangle = ퟏ<br />
× base × height<br />
ퟐ<br />
10. Area of a rectangle = length × breadth<br />
Length = 퐀퐫퐞퐚<br />
퐁퐫퐞퐚퐝퐭퐡<br />
11. Area of a square = side × side<br />
Side of a square = √퐀퐫퐞퐚<br />
12. Area of a parallelogram = Base × Height<br />
13. Area of a rhombus = ퟏ<br />
Breadth= 퐀퐫퐞퐚<br />
퐋퐞퐧퐠퐭퐡<br />
ퟐ × d1 × d2 [where, d1 and d2 are two diagonals]
14. Area of a trapezium = ퟏ<br />
× (a + b) × h [where, 'a' and 'b' are two parallel<br />
ퟐ<br />
sides and 'h' is height]<br />
15. Area of a circle = 훑r 2<br />
16. Lateral Surface Area of a cuboid = 2 × (l + b) × h<br />
Total Surface Area of a cuboid = 2 × (lb + bh + lh)<br />
Diagonal of a cuboid = √퐥 ퟐ + 퐛 ퟐ + 퐡 ퟐ<br />
17. Lateral Surface Area of a cube = 4 × l 2<br />
Total Surface Area of a cube = 6 × l 2<br />
Diagonal of a cube = l√ퟑ<br />
18. Curved Surface Area of a solid cylinder = 2훑퐫퐡<br />
Total Surface Area of a solid cylinder = 2훑r 2 +2훑퐫퐡<br />
= 2훑r (r + h)<br />
Curved Surface Area of a hollow cylinder = 2훑퐑퐡 + 2훑퐫퐡 = 2훑퐡(R + r)<br />
Surface Area of a hollow cylinder = 2훑퐫퐡 + 2훑퐑퐡 + 2(훑R 2 – 훑r 2 )<br />
Area of the ring = 훑R 2 – 훑r 2 = 훑(R 2 – r 2 )<br />
Thickness of the ring = R – r<br />
19. Curved Surface Area of a cone = 훑퐫퐥 [where, l = slant height]<br />
Total Surface Area of a cone = 훑r 2 + 훑퐫퐥 = 훑r (r + l)<br />
20. Surface Area of a sphere = 4훑r 2<br />
Surface Area of a hemisphere = 3훑r 2<br />
21. Surface Area of a prism = 2 × area of base + perimeter of base × height<br />
22. Surface Area of any pyramid = area of base + area of each of lateral faces<br />
23. Surface Area of regular pyramid = area of base + ퟏ<br />
24. Surface Area of square pyramid = b 2 + 2bs<br />
ퟐ<br />
× ps<br />
Where, p = perimeter of the base<br />
s = slant height<br />
[Where, b = length of the base, s = slant height]
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