Triangles
$$A = \tfrac{1}{2}\, b\, h \qquad A = \tfrac{1}{2}\, ab\sin C \qquad A = \sqrt{s(s-a)(s-b)(s-c)},\ \ s=\tfrac{a+b+c}{2}\ \text{(Heron)}$$
Quadrilaterals
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | $l \times w$ | $2(l + w)$ |
| Square | $s^2$ | $4s$ |
| Parallelogram | $b \times h$ | $2(a + b)$ |
| Rhombus | $\tfrac{1}{2}d_1 d_2$ | $4s$ |
| Trapezium | $\tfrac{1}{2}(a + b)h$ | sum of the four sides |
| Kite | $\tfrac{1}{2}d_1 d_2$ | sum of the four sides |
Circle, sector and segment
$$C = 2\pi r = \pi d \qquad A = \pi r^2$$ $$\text{Arc length} = \frac{\theta}{360^\circ}\times 2\pi r \qquad \text{Sector area} = \frac{\theta}{360^\circ}\times \pi r^2$$ $$\text{Segment area} = \frac{\theta}{360^\circ}\pi r^2 - \tfrac{1}{2}r^2\sin\theta$$
Regular polygon with $n$ sides, side $s$, circumradius $r$
$$A = \tfrac{1}{2} n r^2 \sin\left(\frac{360^\circ}{n}\right)$$
Common region of two overlapping circles
Area $=$ sum of the two segments cut off by the common chord.