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Volume of Triangular Pyramid Calculator

Add values into this calculator to calculate the volume of the triangular pyramid.

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Volume of Triangular Pyramid Calculator:

Use this volume of triangular pyramid calculator to get the volume of any triangular pyramid. No matter whether you know about the base value or not, this tool can find the base area and solve for the volume, even if you only have side lengths or other measurements.

Additionally, it allows you to calculate pyramid volume for different types of triangles, including:

  • Equilateral triangles
  • Isosceles triangles ( Input the base length and the height from the base to the apex)
  • Scalene triangles (enter all three side lengths)
  • Right triangular pyramid (a special case of an isosceles triangle with a 90-degree angle at the apex)

Triangular Pyramid:

“A triangular pyramid is a three-dimensional solid shape having four faces as triangles”

Volume of Triangular Pyramid Image:

It has a flat triangular base (equilateral, isosceles, or scalene) and all four sides forming triangles meet at a point called the apex. When all the faces are equilateral triangles, then it is called a tetrahedron.

Parts of A Triangular Pyramid:

  • It consists of 4 faces, 6 edges, and 4 vertices
  • At each vertex, 3 edges meet
  • No parallel faces
  • Variable number of symmetry planes depending on the type of pyramid
  • Triangular based pyramids can be regular (all faces congruent), irregular (faces of different shapes and sizes), or right-angled

What Is The Volume of A Triangular Pyramid?

“The volume of a triangular pyramid is the measure of space enclosed by the pyramid”

The common units that are used for the volume of a triangular pyramid are: \(\ m^{3},\ cm^{3},\ in^{3},\ etc.\) The Volume of Triangular Pyramid Calculator comes with flexibility in handling these all measurement units.

How To Find The Volume of A Triangular Pyramid?

There are two main ways to find the volume, which are:

1. Using the Triangular Pyramid Volume Formula:

\(\ V =\frac{1}{3}\ \times\ Base\ Area\ \times\ Height\) 

Where:

  • V is the volume of the triangular pyramid
  • Base Area is the area of the flat triangular base
  • Height is the distance of the base from the apex (tip) of the pyramid

Solved Example:

Suppose you have a triangular pyramid with a height of 10 centimeters, having a base area of \(\ 25\ cm^{2}\). Find its volume.

Solution:

Given Values:

  • Base Area =\(\ 25\ cm^{2}\)
  • Pyramid Height = 10 cm

Put the values into the equation:

\(\ Volume =\ V = \frac{1}{3}\ \times\ 25\ \times\ 6 = 50 cm^3\)

What If You Don't Know The Base Area?

In this case, you can use any of the following formulas according to the available information:

  • Equilateral Triangle: Base Area = \(\frac{(\sqrt3\ \times\ side\ length^{2})}{4}\)
  • Isosceles Triangle: Area = \(\frac{(base\ length\ \times\text{ height from base to apex})}{2}\) (You will need to have the height from the base to the apex of the triangle)
  • Scalene Triangle: Area =\(\frac{\sqrt{(s(s - a)(s - b)(s - c)}}{4}\) (It needs to know all three side lengths (a, b, c) of the triangle)

Solved Example:

Imagine a triangular pyramid with a known height of 12 centimeters. The base is a triangle, but you only have the length of one side (base) which is 7 centimeters. Now calculate the volume of the pyramid.

Solution:

Given that:

  • Pyramid height = H = 12 cm
  • Side Length = 7 cm
  • Pyramid base = 12 cm

Base Area:

\(\ Base\ Area =\ b = \frac{(7\ \times\ 12)}{2} =\ 42 cm^{2}\)

By adding values in the volume of triangular pyramid formula:

\(\ Volume =\ V = \frac{1}{3}\ \times\ 42\ \times\ 12 = 168 cm^3\)

Note: Always use consistent units (e.g., centimeters, inches) for all values to avoid conversion errors.

2. Using the Triangular Pyramid Volume Calculator:

The most convenient way to find the volume is by using an online calculator, especially if you are not good at mathematics. Whether you are dealing with a small model or a large-scale pyramid, the triangular pyramid volume calculator offers a straightforward and quick way to determine the volume of the triangular pyramids.

Proceed with these steps to make calculations with the calculator:

  • Choose whether the pyramid's base is known or unknown and add values accordingly
  • Click on the “Calculate” button
  • The calculator will show the pyramid volume in various units and the base area if it's unknown

FAQ’s:

What Is the Volume of a Regular Triangular Pyramid?

The formula that is used to calculate the volume of a regular triangular pyramid (also called a tetrahedron) is as follows:

\(\ V =\frac{(a^{3}\ \times\ \sqrt2)}{12}\)

Where:

  • a represents the edge (side length) of the triangular (equilateral) faces.

How Much Is The Volume of The Great Pyramid Gizza?

The Great Pyramid of Giza has an estimated volume of approximately 2.6 million cubic meters (92 million cubic feet). This is an estimate due to erosion and weathering over time but is widely accepted by archaeologists and historians.

What Is The Difference Between A Triangular Prism And A Triangular Pyramid?

  • A triangular prism consists of two bases and the triangular pyramid contains only one base
  • The edges of a pyramid meet at a point while the edges of the faces of a prism are parallel to each other

Reference:

From the source of Wikipedia: Pyramid (geometry), Right pyramids with a regular base

From the source of mathsisfun.com: Triangular Pyramid, Surface Area

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