Geometry Formulas

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

area — base $b$, height $h$

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Heron's formula — $s=\frac{a+b+c}{2}$

$a^2+b^2=c^2$

Pythagorean theorem — $c$ is the hypotenuse of a right triangle

$P=a+b+c$

perimeter

$A=lw$

rectangle — area

$P=2(l+w)$

rectangle — perimeter

$A=s^2$

square — area

$P=4s$

square — perimeter

$A=bh$

parallelogram — base $b$, height $h$

$A=\frac{1}{2}(b_1+b_2)h$

trapezoid — parallel sides $b_1$, $b_2$, height $h$

$A=\frac{1}{2}d_1 d_2$

rhombus — diagonals $d_1$, $d_2$

$C=2\pi r$

circumference

$A=\pi r^2$

area

$s=r\theta$

arc length — $\theta$ in radians

$A=\frac{1}{2}r^2\theta$

sector area — $\theta$ in radians

$V=s^3$

cube

$V=lwh$

rectangular prism

$V=\pi r^2h$

cylinder

$V=\frac{1}{3}\pi r^2h$

cone

$V=\frac{4}{3}\pi r^3$

sphere

$V=\frac{1}{3}Bh$

pyramid — $B$ is the base area

$SA=6s^2$

cube

$SA=2(lw+lh+wh)$

rectangular prism

$SA=2\pi r^2+2\pi rh$

cylinder

$SA=\pi r^2+\pi rl$

cone — $l$ is the slant height

$SA=4\pi r^2$

sphere

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

distance between two points

$M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

midpoint of two points

$m=\frac{y_2-y_1}{x_2-x_1}$

slope between two points

$y=mx+b$

slope-intercept form of a line

$y-y_1=m(x-x_1)$

point-slope form of a line