Perimeter, Area, and Volume
1. The perimeter of a polygon (or any other closed curve, such as a circle) is the distance around the outside.
2. The area of a simple, closed, planar curve is the amount of space inside.
3. The volume of a solid $3\text{D}$ shape is the amount of space displaced by it.
Some formulas for common $2$ dimensional plane figures and $3$ dimensional solids are given below. The answers have one, two, or three dimensions; perimeter is measured in linear units , area is measured in square units , and volume is measured in cubic units .


Shape

Formula

Variables

Square

$P=4s$

$s$ is the length of the side of the square. 
Rectangle

$P=2L+2W$

$L$ and $W$ are the lengths of the rectangle's sides (length and width). 
Triangle

$a+b+c$

$a,b$ , and $c$ are the side lengths. 
$P=a+b+\sqrt{{a}^{2}+{b}^{2}}$

$a$ and $b$ are the lengths of the two legs of the triangle  
Circle


$r$ is the radius and $d$ is the diameter. 


Shape

Formula

Variables

Square


$s$ is the length of the side of the square. 
Rectangle


$L$ and $W$ are the lengths of the rectangle's sides (length and width). 
Triangle

$A=\frac{1}{2}bh$

$b$ and $h$ are the base and height 
Triangle

$\begin{array}{l}A=\sqrt{s\left(sa\right)\left(sb\right)\left(sc\right)}\\ \text{where}\text{\hspace{0.17em}}\text{\hspace{0.17em}}s=\frac{a\text{\hspace{0.17em}}+\text{\hspace{0.17em}}b\text{\hspace{0.17em}}+\text{\hspace{0.17em}}c}{2}\end{array}$

$a$ , $b$ , and $c$ are the side lengths and $s$ is the semiperimeter 
Parallelogram


$b$ is the length of the base and $h$ is the height. 
Trapezoid

$A=\frac{{b}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{b}_{2}}{2}h$

${b}_{1}$ and ${b}_{2}$ are the lengths of the parallel sides and $h$ the distance (height) between the parallels. 
Circle

$A=\pi {r}^{2}$

$r$ is the radius. 


Shape

Formula

Variables

Cube


$s$ is the length of the side. 
Right Rectangular Prism


$L$ is the length, $W$ is the width and $H$ is the height. 
Prism or Cylinder

$V=Ah$ 
$A$ is the area of the base, $h$ is the height. 
Pyramid or Cone

$V=\frac{1}{3}Ah$ 
$A$ is the area of the base, $h$ is the height. 
Sphere


$r$ is the radius. 