Mensuration Formulae

Cheatsheet Content

2D Shapes Square a a Side: $a$ Perimeter: $P = 4a$ Area: $A = a^2$ Diagonal: $d = a\sqrt{2}$ Rectangle l w Length: $l$, Width: $w$ Perimeter: $P = 2(l+w)$ Area: $A = l \times w$ Diagonal: $d = \sqrt{l^2 + w^2}$ Triangle b h Base: $b$, Height: $h$ Area: $A = \frac{1}{2} \times b \times h$ Perimeter: $P = a+b+c$ (sum of sides) Heron's Formula: $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \frac{a+b+c}{2}$ Equilateral Triangle a a a h Side: $a$ Height: $h = \frac{\sqrt{3}}{2}a$ Area: $A = \frac{\sqrt{3}}{4}a^2$ Perimeter: $P = 3a$ Circle r Radius: $r$, Diameter: $d=2r$ Circumference: $C = 2\pi r = \pi d$ Area: $A = \pi r^2$ Parallelogram b h a Base: $b$, Height: $h$, Side: $a$ Area: $A = b \times h$ Perimeter: $P = 2(a+b)$ Trapezoid (Trapezium) $b_1$ $b_2$ h Parallel sides: $b_1, b_2$, Height: $h$ Area: $A = \frac{1}{2}(b_1 + b_2)h$ Perimeter: $P = b_1 + b_2 + c + d$ (sum of all sides) Rhombus a $d_1$ $d_2$ Side: $a$, Diagonals: $d_1, d_2$ Area: $A = \frac{1}{2} d_1 d_2$ Perimeter: $P = 4a$ 3D Shapes Cube a a a Side: $a$ Volume: $V = a^3$ Surface Area: $SA = 6a^2$ Lateral Surface Area: $LSA = 4a^2$ Diagonal: $d = a\sqrt{3}$ Cuboid l w h Length: $l$, Width: $w$, Height: $h$ Volume: $V = lwh$ Surface Area: $SA = 2(lw + wh + hl)$ Lateral Surface Area: $LSA = 2h(l+w)$ Diagonal: $d = \sqrt{l^2 + w^2 + h^2}$ Cylinder h r Radius: $r$, Height: $h$ Volume: $V = \pi r^2 h$ Curved Surface Area: $CSA = 2\pi rh$ Total Surface Area: $TSA = 2\pi r(r+h)$ Cone h r l Radius: $r$, Height: $h$, Slant Height: $l$ $l = \sqrt{r^2 + h^2}$ Volume: $V = \frac{1}{3}\pi r^2 h$ Curved Surface Area: $CSA = \pi rl$ Total Surface Area: $TSA = \pi r(r+l)$ Sphere r Radius: $r$ Volume: $V = \frac{4}{3}\pi r^3$ Surface Area: $SA = 4\pi r^2$ Hemisphere r Radius: $r$ Volume: $V = \frac{2}{3}\pi r^3$ Curved Surface Area: $CSA = 2\pi r^2$ Total Surface Area: $TSA = 3\pi r^2$ Pyramid (Square Base) h b Base side: $b$, Height: $h$, Slant height: $l_s$ Volume: $V = \frac{1}{3} b^2 h$ Lateral Surface Area: $LSA = 2bl_s$ Total Surface Area: $TSA = b^2 + 2bl_s$ $l_s = \sqrt{h^2 + (b/2)^2}$ Prism (Triangular Base) h b $h_T$ Base area: $A_B$, Height: $H$ Volume: $V = A_B \times H$ Lateral Surface Area: $LSA = P_B \times H$ (Perimeter of base $\times$ Height) Total Surface Area: $TSA = P_B H + 2A_B$