Pyramids are three-dimensional figures that are created by a polygon as its base and triangles as its other faces, where all the triangles meet at a common vertex. The fundamental parts of a pyramid are the base, the lateral faces, the height, the slant height, and the vertex or apex.
Here, we will learn more about these parts of the pyramid. We will use a diagram to illustrate the concepts. Then, we will look at the different types of pyramids. Finally, we will learn about the most important formulas of geometric pyramids.
Important parts of a pyramid
The most important parts of a pyramid are:
- Vertex or Apex
- Lateral faces
- Slant height
The base is the polygon in which the pyramid stands. The base can have different geometric shapes. For example, if the base is a triangle, the pyramid is called a triangular pyramid and if the base is a hexagon, the pyramid is called a hexagonal pyramid.
The height of a pyramid is the perpendicular distance from the vertex to the base.
The lateral faces are the faces formed by covering the sides of the base. All lateral faces meet at the vertex and have a triangular shape. The number of lateral faces is equal to the number of sides of the base. For example, a hexagonal pyramid has six lateral faces since its base has six sides.
The slant height is the perpendicular height from the vertex to one of the sides of the base. We can also call this height as lateral height.
Different type of pyramids
There are a great variety of pyramids. We can form different pyramids by using different geometric shapes on the bases. A pyramid is named with respect to the figure at its base. The following are some of the most common pyramids along with their diagrams.
- Triangular pyramid
- Square pyramid
- Rectangular pyramid
- Pentagonal pyramid
- Hexagonal pyramid
Important formulas for pyramids
Pyramids are three-dimensional geometric figures, so their most important formulas are the volume formula and the surface area formula.
The volume of any pyramid is calculated by multiplying the area of its base times the height and dividing the product by three. That is, we have the following formula:
where h represents the length of the height of the pyramid.
Surface area formula
The surface area of any geometric figure is found by adding the areas of all the faces of the figure. Therefore, the surface area of pyramids is equivalent to the sum of the area of the base plus the areas of the lateral faces. The lateral faces are triangles, so we can use the following formula:
where represents the lant height, that is, the height of each triangular face, P represents the perimeter of the base, that is, the sum of all its sides and represents the area of the base.
Interested in learning more about geometric pyramids? Take a look at these pages:
- Volume of a Square Pyramid – Formulas and Examples – Mechamath
- Surface Area of a Square Pyramid – Formulas and Examples – Mechamath
- Volume of a Hexagonal Pyramid – Formulas and Examples – Mechamath
- Surface Area of a Hexagonal Pyramid – Formulas and Examples – Mechamath
- Volume of a Pentagonal Pyramid – Formulas and Examples – Mechamath
- Surface Area of a Pentagonal Pyramid – Formulas and Examples – Mechamath