கணிதம் உங்களுக்காக - 16 - கான்ஸெப்ட்கள்

 1. Area of a parallelogram: A = b × h (where b is the base and h is the height)

2. Perimeter of a parallelogram: P = 2(a + b) (where a and b are the lengths of the sides)

3. Area of a kite: A = ½(d₁ × d₂) (where d₁ and d₂ are the lengths of the diagonals)

4. Perimeter of a kite: P = 2(a + b) (where a and b are the lengths of the pairs of equal sides)

5. Area of a regular hexagon: A = (3√3 / 2) s² (where s is the side length)

6. Perimeter of a regular hexagon: P = 6s (where s is the side length)

7. Area of a regular pentagon: A = (1/4)√(5(5 + 2√5)) s² (where s is the side length)

8. Perimeter of a regular pentagon: P = 5s (where s is the side length)

9. Volume of an oblique cone: V = ⅓πr²h

10. Surface area of an oblique cone: SA = πr(r + √(r² + h²))

11. Volume of a cylindrical shell: V = 2πrh × (R - r) (where R is the outer radius and r is the inner radius)

12. Surface area of a cylindrical shell: SA = 2πh(R + r) (where R is the outer radius and r is the inner radius)

13. Volume of a torus: V = (πr²) × (2πR) = 2π²Rr² (where r is the radius of the tube and R is the distance from the center of the tube to the center of the torus)

14. Surface area of a torus: SA = (2πr) × (2πR) = 4π²Rr

15. Length of a median of a triangle: m = ½ √(2b² + 2c² - a²) (where a, b, and c are the lengths of the sides of the triangle, and m is the median to side a)

16. Length of an altitude in a triangle: h = 2A / a (where A is the area of the triangle and a is the base)

17. Length of an angle bisector in a triangle: l = √(bc[1 - (a² / (b + c)²)]) (where a, b, and c are the lengths of the sides of the triangle, and l is the angle bisector)

18. Area of a cyclic quadrilateral: A = √((s - a)(s - b)(s - c)(s - d)) (where a, b, c, and d are the lengths of the sides, and s is the semi-perimeter)

19. Brahmagupta's formula (area of a cyclic quadrilateral): A = √((s - a)(s - b)(s - c)(s - d) - abcd cos²(½θ)) (where θ is the sum of the opposite angles)

20. Area of an inscribed circle in a triangle: A = r × s (where r is the radius of the inscribed circle and s is the semi-perimeter)

21. Polar to Cartesian coordinates: x = r cos(θ), y = r sin(θ)

22. Cartesian to Polar coordinates: r = √(x² + y²), θ = tan⁻¹(y / x)

23. Slope of the line through points (x₁, y₁) and (x₂, y₂): m = (y₂ - y₁) / (x₂ - x₁)

24. Distance from a point to a line (ax + by + c = 0): d = |ax₁ + by₁ + c| / √(a² + b²) (where (x₁, y₁) is the point)

25. Equation of a line in slope-intercept form: y = mx + c (where m is the slope and c is the y-intercept)

26. General equation of a circle: (x - h)² + (y - k)² = r² (where (h, k) is the center and r is the radius)

27. Parametric equations of a circle: x = h + r cos(t), y = k + r sin(t) (where (h, k) is the center, r is the radius, and t is the parameter)