# Shape Area Calculator

## Using This Calculator

This calculator can be used to quickly figure the area of a triangle, square, rectangle, circle, sphere, pentagon, hexagon, octogon, cube, or cylinder.

For 2 dimensional shapes it calculates the area of the shape & for 3 dimensional shapes it calculates their surface area.

### Area Formulas

The formulas for each regular shape are shown below.

#### Triangle

triangle area = base lenght * height / 2

#### Square

square area = length^{2}

#### Rectangle

rectangle area = length * width

#### Circle

circle ** **area = π * Radius^{2}

#### Sphere

sphere surface area = 4π * Radius^{2}

#### Pentagon

**regular pentagon (without apothem):**side^{2}* 1/4* √(5 (5+2 √5))**regular pentagon (where apothem is known):**area = 5* side * apothem / 2- apothem = 1/2 side / tan 36°

#### Hexagon

hexagon area = side length^{2} * 3 √3 / 2

#### Octagon

octagon area = 2(1+ √ 2) * side length^{2}

#### Cube

cube surface area = 6 * length^{2}

#### Cylinder

cylinder surface area = 2 π * height * Radius+ 2 π * Radius^{2}

## Incircle, Circumcircle, Radius & Apothem

### Definitions

**Regular Polygon:**A polygon with*n*sides where all sides have equal lengths.**Radius:**Line which connects the center of a polygot to one of its verticies.**Circumcircle:**Circle which fits outside a polygon and connects all verticies. The radius of this circle is the same as the radius of the poligon.**Incircle:**Circle which fits inside a polygon and connects the midpoint of each side.**Apothem:**Line connecting the midpoint of a polygon's side to its center.**Perimeter:**The distance around a polygon. For regular polygons with a fixed number of sides this is found by multiplying the length of a side by how many sides the polygon has.**Area:**The amount of space inside the boundary of flat 2-dimensional shapes or the surface of a solid 3-dimensional object.