Hexagonal Pyramid Formula

Hexagonal Pyramid Formula

A Hexagonal Pyramid Formula is a type of pyramid with a hexagonal base and isosceles triangles joining at the apex to form a pyramid. A Hexagonal Pyramid Formula is a three-dimensional structure with a hexagonal base and six isosceles triangle sides. It is sometimes called a heptahedron because it has 7 faces, 12 edges, and 7 vertices. On the Extramarks website, students can learn more about the concept of a hexagonal pyramid.

Hexagonal Pyramid Definition

A hexagonal pyramid is a 3D-shaped pyramid whose base is shaped like a hexagon along the sides or faces of an isosceles triangle, forming a hexagonal pyramid at the apex or vertex. A hexagonal pyramid has a base with six sides along six isosceles triangular faces. Another name for the hexagonal pyramid is the heptahedron. A hexagonal pyramid has 7 faces, 12 edges, and 7 vertices.

Hexagonal Pyramid Properties

Just like every other pyramid, a Hexagonal Pyramid Formula additionally has particular properties that differentiate it from other pyramids.

• A hexagonal pyramid has the bottom of a polygon-formed disk referred to as a hexagon.
• A hexagonal pyramid includes 6 isosceles triangles because the faces are erected towards the bottom and mixed to the apex.
• There are 7 vertices overall in a hexagonal pyramid, of which 6 are at the bottom and one at the top.
• A hexagonal pyramid has 12 edges, i.e. 6 connecting the triangle edges to the primary vertex and the 6 edges of the bottom.
• Overall, a hexagonal pyramid has 7 faces, one for every facet of the triangle in conjunction with one base.

Volume of Hexagonal Pyramid

To calculate the quantity of a Hexagonal Pyramid Formula, students must understand 3 primary components of the hexagonal pyramid i.e. the apothem that’s measured from the middle of the bottom to any factor at the facet of the bottom, 2nd is the length of the bottom, and 1/3 is the peak that’s the peak of the pyramid from the apex to the bottom. Hence, the formulation to calculate the hexagonal pyramid quantity is:

Volume, Hexagonal Pyramid = (a.b.h) cubic units

Where,

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

When the apothem of the hexagonal pyramid is not referred to and while the triangles are equilateral, students are able to use any other formula that is:

Volume of hexagonal Pyramid = (√3/2) × a² × h cubic units,

in which a is the side of the base and h is the height of the hexagonal pyramid

Surface Area Of A Hexagonal Pyramid

Before calculating the surface area of ​​the Hexagonal Pyramid Formula, students also need to know its base. The surface area of ​​a hexagonal pyramid can be calculated given the diagonal height of the pyramid, which is the height from the apex to any point on the boundary of the base of the pyramid. Now students can look at the formulas for the hexagonal pyramid – base and surface area.

Base area of ​​a hexagonal pyramid = 3ab square units

Area of ​​hexagonal pyramid = (3ab + 3bs) square units

Where,

• a is the Apothem
• b is the base
• s is the Slant height of the pyramid

Hexagonal Pyramid Net

A hexagonal pyramid has 7 faces, 7 corners, and 12 sides. A Hexagonal Pyramid Formula network is formed by a six-sided hexagonal base along which six triangles are formed by connecting the edges of the base. These triangles are called the faces of the pyramid. If one flattens the pyramid, one will see 6 triangles and a hexagonal base, that is, 6 faces and 1 face on the base.

Examples on Hexagonal Pyramid Formula

Example 1: Find the volume of a Hexagonal Pyramid Formula with an apothem length of 6 units, a base length of 9 units, and a height of 15 units.

Solution:

If a = 6, b = 9, and h = 15,

Put the values ​​into the volume formula.

The volume of the hexagonal pyramid = dep cubic units

Volume = 6 x 9 x 15

Volume = 810 units³

Therefore, the volume of the given hexagonal pyramid formula is 810 units³.

Example 2: What are the base and surface area of ​​a hexagonal pyramid with a strict length of 4 units, a base length of 9 units, and a bevel height of 14 units? Solution: if a = 4, b = 9, s = 14

Solution:

Floor area = 3ab square units

Footprint = 3x4x9

Floor space = 108 units²

Then calculate the surface area of ​​the Hexagonal Pyramid Formula,

surface area = 3ab + 3bs square units

Area = 3 x 4 x 9 + 3 x 9 x 14

surface = 108 + 378

surface = 486 units²

Example 3: A hexagonal pyramid has a hexagonal base with a side length of 3 meters and a height of 10 meters. Calculate the volume of this hexagonal pyramid.

Solution:

To calculate the volume of a hexagonal pyramid, we use the formula:

\[ V = \frac{1}{3} A_b h \]

where:
\( V \) is the volume.
\( A_b \) is the area of the base.
\( h \) is the height of the pyramid.

The base of the pyramid is a regular hexagon. The area of a regular hexagon with side length \( a \) can be calculated using the formula:

\[ A_b = \frac{3 \sqrt{3}}{2} a^2 \]

Given:
Side length \( a = 3 \) meters.

Plugging in the values:

\[ A_b = \frac{3 \sqrt{3}}{2} (3)^2 \]

\[ A_b = \frac{3 \sqrt{3}}{2} \times 9 \]

\[ A_b = \frac{27 \sqrt{3}}{2} \]

To Calculate the Volume of the Hexagonal Pyramid

Height \( h = 10 \) meters.

Now, use the volume formula for the pyramid:

\[ V = \frac{1}{3} A_b h \]

Plug in the area of the base and the height:

\[ V = \frac{1}{3} \times \frac{27 \sqrt{3}}{2} \times 10 \]

\[ V = \frac{1}{3} \times 135 \sqrt{3} \]

\[ V = 45 \sqrt{3} \, \text{cubic meters} \]

The volume of the hexagonal pyramid is \( 45 \sqrt{3} \) cubic meters.