A triangular pyramid is a geometric solid with a triangular base, and all three lateralfaces are also triangles with a common vertex. The tetrahedron is a triangular pyramid with equilateral triangles on each face. Four triangles form a triangular pyramid.Triangular pyramids are regular, irregular, and right-angled.

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A three-dimensional shape with all its four faces as triangles is known as a triangular pyramid.

1.What isTriangular Pyramid?
2.Types of Triangular Pyramid
3.Propertiesof a Triangular Pyramid
4. Triangular Pyramid Formulas
5. Solved Examples onTriangular Pyramid
6.Practice Questions on Triangular Pyramid
7.FAQs on Triangular Pyramid

What isTriangular Pyramid?


A triangular pyramid is a 3D shape, all of the faces of which are made in the form of triangles. A triangular pyramid is a pyramid with a triangular base and bounded by four triangular faces where 3 faces meet at one vertex. Thebase is a right-angle triangle in a right triangular pyramid, while other faces areisosceles triangles.

Triangular Pyramid Nets

The net patternis different for different types of solids.Nets are usefultofind the surface area of ​​solids. A triangular pyramid netis a pattern that forms when its surface is laid flat, showing each triangular facet of a shape. The triangular pyramid netconsists of four triangles. The base of the pyramid is a triangle; the side faces are also triangles.

Let us do a small activity. Take a sheet of paper.You can observe two differentnets of a triangular pyramidshown below.Copy this on thesheet of paper. Cut it along the edge and fold it as shown in the picture below. The folded paper forms atriangular pyramid.

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Types of Triangular Pyramid


Like any other geometrical figure, triangular pyramids can also be classified into regular and irregular pyramids. The different types of triangular pyramids are explained below:

Regular Triangular Pyramid

A regular triangular pyramidhas equilateral triangles as its faces. Since it is made of equilateral triangles, all itsinternal angles will measure 60°.

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Irregular Triangular Pyramid

An irregular triangular pyramidalso has triangular faces, but they are not equilateral. The internalangles in each plane add up to 180° as theyare triangular. Unless a triangular pyramidis specificallymentioned asirregular,all triangular pyramidsare assumed to beregular triangular pyramids.

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Right Triangular Pyramid

The right triangular pyramid (a three-dimensional figure) has a right-angle triangle base and the apex aligned above the center of the base. It has1 base, 6 edges, 3 faces, and 4 vertices.

Important Notes

A triangular pyramidhas 4 faces, 6 edges, and 4 vertices.All four faces are triangular in shape.

Propertiesof a Triangular Pyramid


Properties of a triangular pyramid help us to identify a pyramid from a given set of figures quickly and easily. The different Propertiesof a Triangular Pyramid are:

It has 4 faces, 6 edges, and 4 vertices.At each of its vertex, 3 edges meet.A triangular pyramidhas no parallel faces.Triangular Pyramidsare found asregular, irregular, and right-angled.

Triangular Pyramid Formulas

There are various formulas to calculate the volume, surface area, and perimeter of triangular pyramids. Those formulae are given below:


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To find the volume of a pyramidwith a triangular base, multiply the area of ​​the triangular base by the height of the pyramid (measured from base to top). Then divide that product by three.

Triangular PyramidVolume = 1/3 × Base Area × Height

The slant height of a triangular pyramid is the distance from its triangular base along the center of the face to the apex.To determine the surface area of ​​a pyramid with a triangular base, add the area of ​​the base and the area of ​​all sides.

Triangular Pyramid Surface Area(Total) = Base Area + 1/2(Perimeter × Slant Height)


Now consider a regular triangular pyramidmade of equilateral triangles of side a.


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Regular Triangular Pyramid Volume = a3/6√2

Regular Triangular PyramidSurface Area(Total) = √3a2

Right Triangular Pyramid Formulas

Surface AreaofaRight Triangular Pyramid ((A_s)) = 1/2 ((h_b) × a) + 3/2 (a × (h_s))

The volume of a Right Triangular Pyramid (V) = 1/6× (h_b) × a × h = 1/3× (A_b) × h

Where (A_s) = Surface Area,(A_b) = Base Area, V= Volume, a= Edge, h= Height,(h_b) = Height Base, and(h_s) = Height Side.

Challenging Questions:

Rohan hasa tent that is shaped likean irregular triangular pyramid. The volume of the tent is v cubic cm, and the height is h cm. What would be the areaof the base of histent?

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Example 1: Sid got to know that two triangular pyramids were congruent.He startedobserving themfor their congruency. While he placed the base of both the triangles in a position to see if theyoverlap, the two congruent triangular pyramidsstuck together along its base andformed a triangular bipyramid. How many faces, edges, and vertices does this bipyramid have?

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Solution: If we openup theabove image to see the net of the triangular bipyramid,we can observe this:

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There are6 triangular faces, 9 edges, and 5 vertices. ∴ Triangular bipyramid has 6 triangular faces, 9 edges, and 5 vertices.

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Example 2: Find the volume of a regular triangular pyramidwith a side length measuring5 units. (Round off the answer to 2 decimal places)

Solution: We know that for a triangular pyramidwhose side is a volume is:a3/6√2. Substituting a = 5, we get

Volume = 53/6√2

= 125/8.485

≈14.73

∴The volume of thetriangular pyramid is 14.73 units3


Example 3: Each edge of a regular triangular pyramidis of length 6 units. Find its total surface area.

Solution: The total surface area of a regular triangular pyramidof side ais:√3a2. Substituting a= 6, we get,

TSA =√3 × 62= √3 × 6 × 6

= 62.35

∴ Total Surface Area = 62.35 units2


Example 4: While solving questions about the triangular pyramid,Syna got stuck. Let's help her out to reach the final answer. Here's the question:"The sum of the length of the edges of a regular triangular pyramidis 60 units. Find the surface area of one of its faces."

Solution: We know that atriangular pyramidhas 6 edges. And it's given to be a regular triangular pyramid. Therefore, the length of each edge is:60/6 = 10units. The surface area of one face of the triangular pyramid: