Hexagonal Pyramid

A hexagonal pyramid is a three-dimensional geometric shape with a hexagonal base and six triangular faces that meet at a single point called the apex.

• Base: The base is a hexagon (a polygon with six sides).
• Apex: The point above or below the base where all triangular faces converge.

A hexagonal pyramid will have 6 isosceles triangles as lateral faces only if the apex is positioned symmetrically above or below the center of the hexagon. Otherwise, the lateral faces may not be isosceles.

Some of its Key Characteristics are:

Faces: It has 7 Faces:

• 6 triangular faces connecting the apex to each side of the hexagon.
• 1 hexagonal base.

Vertices: It has 7 vertices:

• 6 vertices on the hexagonal base.
• 1 vertex at the apex.

Edges: It has 12 edges:

• 6 edges of the hexagonal base.
• 6 edges connecting the base vertices to the apex.

Hexagonal pyramid is also sometimes known as Heptahedron as it has seven faces, 12 edges, and 7 vertices.

Read More:

• Polygons
• Hexagon
• Isosceles

Hexagonal Pyramid Formula

Formula of volume for Hexagonal Pyramid
The volume of a hexagonal pyramid is given by the apothem (length from the center of the base to any point on the base), length of the base, and height of the pyramid. The height of the pyramid is measured from the apex to the base.

Hence, the volume formula for the calculation of the volume of the hexagonal pyramid is given by the product of apothem, length of base, and height.
Mathematically, the formula is written as,

The volume of Hexagonal Pyramid = a × b × h 

Where,

• a is the apothem of the pyramid
• b is the base
• h is the height

There is also an alternate formula for the calculation of the volume of the pyramid in case of the absence of apothem and the given triangles of the pyramid are equilateral.
The formula is given by

The volume of Hexagonal Pyramid = (√3/2) × a²× h

 Where,

•  a is the side of the base.
• And h is the height of thehexagono.nal pyramid.

The formula of surface area for the Hexagonal pyramid

The surface area of a hexagonal pyramid is given by the apothem of the pyramid, base, and slant height of the pyramid. The slant height of the pyramid is measured from the apex to any point on the boundary of the base of the pyramid.

For the calculation of the surface area of the hexagonal pyramid, there is also a need to look into the formula of the base area. Hence, the formulas for base area and surface area are mentioned below respectively.

Base Area of Hexagonal Pyramid = 3ab

Surface Area of Hexagonal Pyramid = (3ab + 3bs)

Where,

• a is the apothem of the pyramid.
• b is the base.
• s is the slant height of the pyramid.

Regular and Irregular Hexagonal Pyramid

A regular hexagonal pyramid has a regular hexagonal base (where all sides and angles of the hexagon are equal), and the apex (the top point) is directly above the center of the hexagonal base.

• The base is a regular hexagon with equal side lengths and angles.
• The lateral faces are isosceles triangles (with two equal sides from the apex to the base).
• The apex is symmetrically above the center of the hexagonal base.
• The lateral edges (edges from the apex to the base) are all equal in length.

An irregular hexagonal pyramid has an irregular hexagonal base (where the sides and angles of the hexagon are not equal), and the apex may be positioned anywhere above the base, not necessarily symmetrically above the center.

• The base is an irregular hexagon with unequal sides and angles.
• The lateral faces are scalene triangles, as the distance from the apex to different vertices of the base may vary.
• The apex is not necessarily above the center of the base, which leads to an asymmetrical shape.
• The lateral edges (edges from the apex to the base) can have different lengths.

Net of a Hexagonal Pyramid

The net of a hexagonal pyramid consists of:

• 1 hexagonal base.
• 6 isosceles triangles (or possibly scalene, depending on the apex position), form the lateral faces.

These shapes are arranged flat in a two-dimensional layout, and when folded along the edges, they form a three-dimensional hexagonal pyramid. The triangles are attached to the sides of the hexagon, and the apex is where all the triangles meet.

Related Reads,

• Pyramid
• Triangular Pyramid
• Pentagonal Pyramid

Solved Questions on Hexagonal Pyramid

Question 1: Calculate the volume of a hexagonal pyramid with an apothem length of 3cm, base length of 4cm, and height of 5cm.
Solution:

Given:
Apothem length is 3cm.
Base length is 4cm.
Height is 5cm.

Now,
Hexagonal pyramid volume = a × b × h
=> Volume = 3 × 4 × 5
=> Volume = 60cm³

Question 2: Calculate the base area and surface area of a hexagonal pyramid, if the apothem length is 4cm, the base length is 8cm and the slant height is .2cm?
Solution:

Given:
Apothem length is 4cm.
Base length is 8cm.
Slant height is 12cm.

Now,

Base area = 3ab
=> Base area = 3 × 4 × 8
=> Base area = 96cm²

Then,
Surface area = (3ab + 3bs)
=> Surface area = (96 + 3 × 8 × 12)
=> Surface area = 96 + 288
=> Surface area = 384cm²