Custom Thermoelectric - Peltier

Geometric

 Formulas for Calculating Area and Volume


 

Area of Triangle, Acute

image of acute triangle with known base and height

image of formula for calculating the area of a triangle

 


Area of Triangle, Right

image of right triangle with known base width and height

formula for area of triangle if base width and height are known

 


Area of Triangle, Obtuse

image of obtuse triangle with known base width and height

formula for calculating area of obtuse triangle

 


Area of Triangle, 3 side lengths known Also known as Heron's formula

image of triangle where the length of all 3 sides is known

image of Herons formula for calculating the area of a triangle when the length of 3 sides is known

 


Area of a Rectangle

image of rectangle

formula for area of rectangle

 


Area of Regular Polygons (Any number of sides)

image of regular 6 sided polygon with side length and apothem labeled

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.

formula for calculating the area of any regular polygon if length of side is known

 


Volumes


Volume and Surface Area of a Sphere

image of sphere for calculating area and volume of a sphere

image of formula for volume and surface area of sphere



Volume and Surface Area of a Rectangular Prism (box)

image of rectangular prism or box

image of formula for the volume and surface area of a rectangular box



Volume and Surface Area of a Cube

image of cube with known side length

image of formula used to calculate volume and surface area of a cube with known side length



Volume and Surface Area of a Right Cone

image of right cone with known height and radius

image of formula for the volume and surface area for a right cone



Volume and Surface Area of a Right Cylinder

image of right cylinder with known height and radius

image of formula for the volume and surface area for a right cylinder

 


 Volume and Surface Area of a Right Pyramid (any number of sides)

 image of 3 sided pyramid with known height and side length image of 4 sided pyramid with known side length and height

image of 5 sided pyramid with known side length and height image of 11 sided pyramid with known side length and height

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.

image of formula for the volume and surface area for a right pyramid

 


Volume and Surface Area of a Regular Tetrahedron

image of regular tetrahedron with known side length

image of formula for the volume and surface area for a tetrahedron

 


Volume and Surface Area of a Regular Octahedron

image of octahedron with known side length

image of formula for the volume and surface area for a octahedron



Volume and Surface Area of a Regular Dodecahedron

image of dodecahedron with length of side known

image of formula used to calculate the volume and surface area of a dodecahedron with only the length of a side known



Volume and Surface Area of a Regular Icosahedron

image of icosahedron with known side length

image of formula for calculating the volume and surface area of an icosahedron



Volume of a Partially Filled Lying down Cylinder

image of partially filled cylinder in a horizontal position

image of formula for calculating volume of a partially filled cylinder in a horizontal position



Volume of a Barrel

image of a barrel with known middle and end radius

image of formula for volume of a barrel



Volume and Surface Area of an Ellipsoid

image of an ellipsoid with known lengths of each radius

image of formula for calculating the volume and surface area of an ellipsoid



Volume and Surface Area of a Torus (doughnut shape)

image of a torus or doughnut

 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.

image of formula used to calculate the volume and surface area of a torus or doughnut