Pyramid (triangle base) - Weight

The Weight or Mass of a Triangle Based Pyramid calculator computes the mass (M) of a pyramid with a triangle base that is defined by the length of the three triangle base sides (a,b,c) and height (h) from the base to the apex.  The mass is computed using the volume and the mean density of the composition of the pyramid.  
INSTRUCTIONS:

• (a) Length of side a
• (b) Length of side b 
• (c) Length of side c
• (h) Height of pyramid
• (mD) Mean density of the composition of the pyramid.  (e.g. 2,400 kg/m³ for concrete)

Mass of the Pyramid (M): The mass is returned in kilograms, and the volume in cubic meters.  However, these can be automatically converted to compatible units via the pull-down menu.  

The Math / Science

The formula for the mass of a triangle based pyramid is:

`m = mD * 1/3 * h * sqrt((a+b+c)/2((a+b+c)/2-a)((a+b+c)/2-b)((a+b+c)/2-c))`

where:

• m = mass of pyramid
• h = height of pyramid
• a,b,c = sides of the triangle base

Note: this implies that the height is normal to triangle plane. 

Mean Density Table

Mean density is scientifically volume divided by mass.  There are  various unit for density adopted by cultures and industries. Common units for density included the following:

• kilograms per cubic meter (kg/m³)
• grams per cubic centimeter (g/cm³)
• grams per liter (g/L)
• pounds per cubic feet (lb/ft³)
• ounces per cubic inch (oz/in³)
• pounds per barrel (lb/bbl)
• pounds per bushel (lb/bu)

If you want to identify a material by its density, use the Density Within Range tool.

Other Related Calculators

• To lookup the mean density of over 500 materials, CLICK HERE.
• To compute the Area of a Triangle with Three Different Sides, CLICK HERE. 
• To compute the Volume of a Triangle Based Pyramid, CLICK HERE.