This page presents the most important geometry formulas for area, perimeter, circumference, volume, and surface area of common plane figures and solid shapes.
Right Triangle and Pythagorean Theorem
For a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\):
\[ a^2 + b^2 = c^2 \]
Plane Figures: Area and Perimeter
Triangle
Perimeter:
\[ P = a + b + c \]Area formulas:
Using base \(b\) and height \(h\):
\[ A = \frac{1}{2} b h \]Using two sides and the included angle:
\[ A = \frac{1}{2} bc \sin A, \quad A = \frac{1}{2} ac \sin B, \quad A = \frac{1}{2} ab \sin C \]Heron's Formula (when all three sides are known):
\[ A = \sqrt{s(s-a)(s-b)(s-c)}, \quad s = \frac{a+b+c}{2} \]Rectangle
Parallelogram
Trapezoid
Circle & Circular Sector
Circle:
\[ C = 2\pi r \] \[ A = \pi r^2 \]
Circular Sector (central angle \(t\) in radians):
\[ s = r t \] \[ A = \frac{1}{2} r^2 t \]Solid Shapes: Volume and Surface Area
Rectangular Solid (Rectangular Prism)
Sphere
Right Circular Cylinder
Right Circular Cone
