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Maths > Basic Geometrical Ideas > Triangular Pyramid – Properties, Volume, Faces, Edges
Basic Geometrical Ideas

Triangular Pyramid – Properties, Volume, Faces, Edges

Introduction to Triangular Pyramid 

Triangular pyramid refers to a polyhedron that comprises six straight edges, four vertex corners, and four triangular faces. Furthermore,  it happens to be the simplest of all the ordinary convex polyhedra. Moreover, it is the only ordinary convex polyhedra that have fewer than five faces.

In this topic, you will learn about triangular pyramids. Also, you will be able to learn the properties, volume, faces, and Edges of this figure.

triangular pyramid

What is Triangular pyramid

On hearing the word pyramid, the first thing that comes to mind is the Great Pyramid of Giza, Egypt. But, if you look at the picture of the pyramids from the above then you will find that these are square pyramids and not triangular pyramids.

So, the bigger question is what are triangular pyramids? The answer is simple, the triangular pyramid is polyhedron or a 3-D (three dimensional) shape that has at least three sides and a polygonal base. Also, it has six edges, and four vertices or points.

Besides, there are also other pyramids like pentagonal, rectangular, hexagonal, and square pyramids. Moreover, these pyramids have a pentagon, rectangle, hexagon, and square as its base respectively.

Parts of a triangular pyramid

A triangular pyramid has three main components. First is, of course, its base, second is its face, the third, and last is the top point of the pyramid which is also known as apex. Also, at the apex, all the faces of the triangle meet.

Besides, in a triangular pyramid, there is some important measurement that includes the base length apothem, height, length, and the slant height of the triangular pyramid. In addition, many of you question what is apothem length, and slant height.

So, slant height is the length of one side of the triangle. Also, the apothem length is the line that goes perpendicular from the point of the triangle to the base of the triangle.

Properties of Triangular Pyramid

The various properties of the triangular pyramid include:

  • It is a polyhedron and more specifically it is a tetrahedron.
  • Moreover, it has 4 faces (3 side faces and a base face).
  • Furthermore, the base of the triangular pyramid is also a triangle.
  • Besides, it has 4 vertices (points) and 6 edges.
  • All the side faces of the pyramid meet at the top which is known as the apex.
  • Most noteworthy, all the triangular pyramids have one common property that all their sides are triangular.

Faces of Triangular Pyramid

The triangular-based pyramids face solely form the triangles. Also, three triangular sides slant upwards from the triangular base. Moreover, its forms of four triangles which also include one triangular base so it can be known as a tetrahedron.

Moreover, if all the faces of the triangular pyramid are equilateral triangles or triangles whose edges are of the same length, then we call these pyramids regular tetrahedron. And, if the triangles have edges of different length then they are termed as an irregular tetrahedron.

Edges of Triangular Pyramid

In a triangular based pyramid, there are six edges, three alongside the base and three prolonged from the base. Furthermore, if the length of the six edges is equal, then all the triangles are equilateral and the pyramid is a regular tetrahedron.

The volume of Triangular Pyramid

For knowing the volume of the triangular pyramid, multiply the area of the triangular base with the height of the pyramid and then divide the number by 3.

Volume = 1/3 × [Base Area] × Height
Example: Now suppose that the base area of the pyramid is 40 and the height of the pyramid is 10. Find its volume.
Volume = 1 / 3 × [Base Area] × Height
Volume = 1 / 3 × [Base Area] × Height
= 1 / 3 × 40 ×10
= 1 / 3 × 400
= 400 / 3
= 133.33

Solved Question for You

Question. What will be the volume of the triangular pyramid if its height is 5 cm and its base area is 30 cm?

A. 40 cm3
B. 50 cm3
C. 60 cm3
D. 51 cm3

Answer. The correct answer is option B.
Solution:
Volume = 1 / 3 × [base area] × height
Volume = 1 / 3 × 30 × 5, = 1 / 3 × 150 =150 / 3, = 50 cm3

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