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Length x Width

Side x Side or Side^2

$\pi r^2$

0.5 x Base x Height

Base x Height

0.5 x (Base1 + Base2) x Height

$\pi a b$

0.5 x Diagonal1 x Diagonal2

0.5 x Diagonal1 x Diagonal2

Depends on the type of polygon

$\frac{3\sqrt{3}}{2} s^2$

$\frac{\sqrt{3}}{4} s^2$

$0.5 r^2 \theta$ (where $\theta$ is in radians)

$\frac{1}{4}\sqrt{5(5+2\sqrt{5})} s^2$

$\pi (R^2 - r^2)$

Area cannot be determined from diagonals alone

$\sqrt{s(s-a)(s-b)(s-c)}$ where $s = \frac{a+b+c}{2}$ (Heron's formula)

$2(1+\sqrt{2})s^2$

$4\pi r^2$