# Geometric

Formulas for Calculating Area and Volume

Area of Triangle, Acute  Area of Triangle, Right  Area of Triangle, Obtuse  Area of Triangle, 3 side lengths known Also known as Heron's formula  Area of a Rectangle  Area of Regular Polygons (Any number of sides) First find the apothem, which is the distance from the center of the polygon to the midpoint of any side. If the apothem is unknown, then calculate it based on knowing the length of a side L and the number of sides n. Volumes

Volume and Surface Area of a Sphere  Volume and Surface Area of a Rectangular Prism (box)  Volume and Surface Area of a Cube  Volume and Surface Area of a Right Cone  Volume and Surface Area of a Right Cylinder  Volume and Surface Area of a Right Pyramid (any number of sides)    First find the area of the base B and the perimeter of the base P.  Use the "Area of a regular Polygon" formula from above if needed.

To calculate the surface area, first calculate the Slant Height s, then calculate the areas using the following formulas. Volume and Surface Area of a Regular Tetrahedron  Volume and Surface Area of a Regular Octahedron  Volume and Surface Area of a Regular Dodecahedron  Volume and Surface Area of a Regular Icosahedron  Volume of a Partially Filled Lying down Cylinder  Volume of a Barrel  Volume and Surface Area of an Ellipsoid  Volume and Surface Area of a Torus (doughnut shape) Where R is the distance from the center of the tube to the center of the Torus and r is the radius of the tube. 