Video lectures
Formulae (Mathematics - Basic)
Area and perimeter of a rectangle
Perimeter of rectangle = 2(l+b)
Area of a rectangle = l×b
Diagonal of a rectangle = `\sqrt{l^2+b^2}`
Area and perimeter of a square
Perimeter of a square = 4a
Area of a square = `(side)^2` or,`1/2×(diagonal)^2`
Diagonal of a square = `\sqrt{2}a`
Area and perimeter (circumference) of a circle
Circumference of a circle = 2𝜋r
Area of a circle = 𝜋`r^2`
Area of a triangle
Area of a triangle = `1/2× base × height`
Area of a right angle triangle = `1/2×`product of its legs
Area of an equilateral triangle = `\sqrt3/4a^2`
Area of an isosceles triangle = `1/2 × b× \sqrt{a^2 - b^2/4}`
If a, b, c are the sides of a `\triangleABC` and s = `1/2(a+b+c)`, then
area of `\triangleABC = \sqrt{s(s-a)(s-b)(s-c)}` (Heron's formula)
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Area of a parallelogram = base `×` height
Area of a rhombus = `1/2×` product of diagonals
Area of a trapezium = `1/2 ×` sum of parallel sides `×` distance between them
or, `1/2 (a+b)×h`
Volume and surface area of solids
Cuboid
Volume of a cuboid = `l × b × h`
Diagonal of a cuboid = `\sqrt {l^2 + b^2 + h^2}`
Total surface area of a cubod = `2(lb+bh+lh)`
Lateral surface area of a cuboid = `2(l+b)×h`
Cube
Volume of a cube = `a^3`
Diagonal of a cube = `\sqrt3a`
Total surface of a cube = `6a^2`
Lateral surface area of a cube = `4a^2`
Cylinder
Volume of a cylinder = 𝜋`r^2`h
Curved (lateral) surface area of a cylinder = 2𝜋rh
Total surface area of a cylinder = 2𝜋r(h+r)
Right circular cone
Slant height `l` = `\sqrt{\h^2 + r^2}`
Volume of the cone = `1/3`𝜋`r^2h`
Curved surface area of a cone = 𝜋`rl`
Total surface of a cone = 𝜋`rl` +𝜋`r^2` = 𝜋`r(l+r)`
Work in progress ......
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Formulae
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