Geometry Area and Volume Formulas

Study Notes

Area of a rectangle/parallelogram: ( A = bh ) (base × height)
Area of a triangle: ( A = \frac{1}{2}bh ) (half the base × height)
Area of a trapezoid: ( A = \frac{(b_1 + b_2)h}{2} ) (average of the two bases × height)
Area of a circle: ( A = 3.14r^2 ) (π times the radius squared)

Surface area of a rectangular prism: ( SA = 2lw + 2lh + 2wh ) (sum of areas of all faces)
Surface area of a triangular prism: ( SA = 2B + Ph ) (2 times the base area plus perimeter times height)
Surface area of a cylinder: ( SA = 2(3.14)r^2 + 3.14dh ) (top and bottom areas plus the lateral area)
Surface area of a pyramid: ( SA = \frac{1}{2}Pl + B ) (half the perimeter times slant height plus base area)
Surface area of a cone: ( SA = 3.14rl + B ) (lateral area plus base area)
Surface area of a sphere: ( SA = 4(3.14)r^2 ) (surface area in terms of radius)

Volume of a prism: ( V = Bh ) (base area times height)
Volume of a cylinder: ( V = 3.14r^2h ) (base area (circle) times height)
Volume of a cone/pyramid: ( V = \frac{1}{3}Bh ) (one-third of the base area times height)
Volume of a sphere: ( V = \frac{4}{3}(3.14)r^3 ) (proportional to the cube of the radius)

Formula for simple interest: ( I = prt ) (interest equals principal times rate times time)
Formula for compound interest: ( B = p(1 + r)^t ) (final balance calculated on principal plus interest)