Ellipse Formula:
Area of Ellipse: [ π×r1×r2 ]
Volume of Ellipse: [ (4/3)×π×r1×r2×r3 ]
Perimeter of Ellipse: [ 2×π×Sqrt((r1² + r2²)/2) ]
Where
r1, r2, and r3 are radii
Sphere Formula:
Volume of Sphere = (4/3)πr³
Curved Surface Area(CSA) of Sphere = 4πr²
where
r = radius
Cylinder Formula:
Volume of Cylinder = πr²h
Curved Surface Area(CSA) of Cylinder = 2πrh
Total Surface Area(TSA) of Cylinder = 2πr(h + r)
where
r = radius, h = height
Cube Formula:
Volume of Cube = a³
Surface Area of Cube = 6a²
Diagonal of Cube = Sqrt(3)*a
where
a = side
Hemisphere Definition:
A hemisphere is half of a sphere.
Hemisphere Formula:
Volume of Hemisphere = (2/3)πr³
Curved Surface Area(CSA) of Hemisphere = 2πr²
Total Surface Area(TSA) of Hemisphere = 3πr²
where
r = radius
Cone Formula:
Slant height of Cone(l) = Sqrt(r² + h²)
Volume of Cone = (1/3)πr²h
Curved Surface Area(CSA) of Cone = πrl
Total Surface Area(TSA) of Cone = πr(l + r)
where
r = radius, l = slant height, h = height
Circle Formula:
Area of Circle = πr²
Diameter of Circle = 2r
Circumference of Circle = 2πr = πd
Area of Sector = πr²(θ/360)
where
r = radius
Pyramid Definition:
A pyramid is a polyhedron with one face as base, a polygon and all the other faces triangles meeting at a common polygon vertex as the apex.
Triangular Pyramid Definition:
A Triangular Pyramid is a pyramid having a triangular base.
Triangular Pyramid Formula:
Area of Base(A) = ½ * a * s
Surface Area of Pyramid = (½ * a * s) + ((3/2)sl) = A + ((3/2)sl)
Volume of Pyramid = (1/6)abh
where
a = apothem length, s,b = side, h = height and l = slant height
Prism Definition:
A prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides.
Triangular Prism Definition:
A Triangular Prism is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
Triangular Prism Formula:
Area of Base(A) = ½ * a * b
Perimeter of Base(P) = s1 + s2 + s3
Surface Area of Prism = ab + (s1 + s2 + s3)h = ab + Ph
Volume of Prism = ½ * a * b * h = Ah
where
a = altitude, b = base, h = height and s1, s2, s3 are sides
Polygon Definition:
A polygon is a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments.
Polygon Formula:
Using length of a side :
Area of Polygon = ((side)² * N) / (4Tan(π / N))
Perimeter of Polygon = N * (side)
Using radius (circumradius) :
Area of Polygon = ½ * R² * Sin(2π / N)
Using apothem (inradius) :
Area of Polygon = A² * N * Tan(π / N)
where A = R * Cos(π / N)
Using apothem and length of a side :
Area of Polygon = (A * P) / 2
where A = side / (2 * Tan(π / N))
where,
N = Number of sides, A = Apothem, R = Radius, P = Perimeter
Trapezium/Trapezoid Formula:
Area of Trapezium = ½×(a + b)×h
where
a, b = sides, h = height
Perimeter of Trapezium = a + b + c + d
where
a, b, c, d = sides
Rhombus Formula:
Base Times Height Method : Area of Rhombus = b * h
Diagonal Method : Area of Rhombus = ½ * d1 * d2
Trigonometry Method : Area of Rhombus = a² * SinA
Perimeter of Rhombus = 4(a)
where
a = side, b = breadth, h = height, d1, d2 are diagonals
Equilateral Triangle Definition:
Equilateral triangle is a triangle that has equal length on all three sides.
SAS Triangle Definition:
If two sides and the included angles of two triangles are correspondingly equal, the two triangles are congruent. This is called SAS Triangle.
Triangle Formula:
Area of Triangle = l * b
Perimeter of Triangle = a + b + c
Area of Equilateral Triangle = (Sqrt(3) / 4) * l²
Area of SAS Triangle = ½ * l * b * SinC
where
l = length, b = breadth
a, b, c = sides of triangle
Rectangle Formula:
Area of Rectangle = b×h
Perimeter of Rectangle = 2(b) + 2(h)
where
b = breadth, h = height
Square Formula:
Area of Square = (a)²
Perimeter of Square = 4(a)
Diagonal of Square = (a)(sqrt(2))
where
a = side
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