CKS Study

Basic Geometry Formulas Perimeter of a Square = P = 4a Where a = Length of the sides of a Square Perimeter of a Rectangle = P = 2(l+b) Where, l = Length ; b = Breadth Area of a Square = A = a 2 Where a = Length of the sides of a Square Area of a Rectangle = A = l×b Where, l = Length ; b = Breadth Area of a Triangle = A = ½×b×h Where, b = base of the triangle ; h = height of the triangle Area of a Trapezoid = A = ½×(b 1  + b 2 )×h Where, b1 & b2 are the bases of the Trapezoid ; h = height of the Trapezoid Area of a Circle = A = π×r 2 Circumference of a Circle = A = 2πr Where, r = Radius of the Circle Surface Area of a Cube = S = 6a 2 Where, a = Length of the sides of a Cube Curved surface area of a Cylinder  = 2πrh Total surface area of a Cylinder = 2πr(r + h) Volume of a Cylinder = V = πr 2 h Where, r = Radius of the base of the Cylinder ; h = Height of the Cylinder Curved surface area of a cone =  πrl Total surface area of a cone = πr(r+l) = πr[r+√(h 2

credit:third party image reference (a + b) 2  = a 2  + 2ab + b 2 (a – b) 2  = a 2  – 2ab + b 2 a 2  – b 2  = (a + b)(a – b) a 2  + b 2  = (a + b) 2  – 2ab (a + b + c) 2  = a 2  + b 2  + c 2  + 2ab + 2bc + 2ca (a + b) 3  = a 3  + 3a 2 b + 3ab 2  + b 3  ; (a + b) 3  = a 3  + b 3  + 3ab(a + b) (a – b) 3  = a 3  – 3a 2 b + 3ab 2  – b 3 a 3  – b 3  = (a – b)(a 2  + ab + b 2 ) a 3  + b 3  = (a + b)(a 2  – ab + b 2 ) (a + b) 4  = a 4  + 4a 3 b + 6a 2 b 2  + 4ab 3  + b 4 (a – b) 4  = a 4  – 4a 3 b + 6a 2 b 2  – 4ab 3  + b 4 a 4  – b 4  = (a – b)(a + b)(a 2  + b 2 ) a 5  – b 5  = (a – b)(a 4  + a 3 b + a 2 b 2  + ab 3  + b 4 ) a 3  +  b 3  +  c 3  -  3abc  = (a +  b  +  c )(a 2  +  b 2  +  c 2  - ab - bc - ca)