Hexagonal Pyramid Formula
Hexagonal Pyramid Formula
Geometry is an important academic theme in Mathematics. This discipline focuses on Morphology and Structure. Geometry describes a shape, its dimensions, properties, and perimeters, and also provides mathematical formulas that facilitate the calculation of these parameters. Students can read reference materials on the Extramarks website which describe a fixed-form Hexagonal Pyramid Formula. The academic content available on the Extramarks website consists of the definition of the Hexagonal Pyramid Formula and its properties. Extramarks’ study materials also contain formulas for calculating the parameters and solving mathematical problems to understand how they are calculated.
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. A Hexagonal Pyramid Formula is sometimes called a heptahedron because it has 7 faces, 12 edges, and 7 vertices. In summary, a Hexagonal Pyramid Formula is a three-dimensional structure with a six-sided base and face composed of six isosceles triangles that meet at the vertices. A Hexagonal Pyramid Formula is another type of pyramid that exists. A Hexagonal Pyramid Formula has a hexagonal-shaped base with an isosceles triangle as the face connecting the pyramid at the apex. 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 shape 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. Students can peruse what are these properties:
- A hexagonal pyramid has the bottom of a polygon-formed discern 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 of the pyramid and one on 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
a is the apothem of the pyramid
b is the bottom
h is the peak
When the apothem of the hexagonal pyramid is not referred to and while the triangles are equilateral, students are able to use any other opportunity formulation that is:
Volume of hexagonal Pyramid = (√3/2) × a2 × h cubic units, in which a is the facet of the bottom and h is the peak 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.
The base area of a hexagonal pyramid = 3ab square units
Area of hexagonal pyramid = (3ab + 3bs) square units
a is the pyramid apex
b is the base
s is the diagonal 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.
Hexagonal Pyramid Related Topics
Below are some interesting topics related to the Hexagonal Pyramid Formula concept.
- area of hexagon
- Pyramid volume
- Area of polygon
- square pyramid
- triangular pyramid
Examples On Hexagonal Pyramid
- 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, plug the values into the volume formula.
The volume of the hexagonal pyramid = dep cubic units
Volume = 6 x 9 x 15
Volume = 810 units 3
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
First, students must calculate the area of the base of the Hexagonal Pyramid Formula.
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 units 2
Therefore, the face of the pyramid is 486 units 2 and the base is 108 units 2.
- Example 3. What is meant by the Properties of the Hexagonal Pyramid Formula?
The base of the hexagonal pyramid is a hexagon and consists of faces made up of six isosceles triangles. The isosceles triangles that make up the face are erect and meet at the vertices and the hexagonal pyramid has 7 faces, 12 edges, and 7 vertices.
- Example 4. What will be the Formula for the volume of a hexagonal pyramid
The volume of a hexagonal pyramid is given by the aposem (the length from the center of the base to any point on the base), the length of the base, and the height of the pyramid. The height of the pyramid is measured from top to bottom.
So the volume formula for calculating the volume of a hexagonal pyramid is the product of the aposem, the length of the base, and the height.
Mathematically, the formula is written as:
The volume of hexagonal pyramid＝a×b×h
Hexagonal Pyramid Practice Questions
- What is a hexagonal pyramid?
A hexagonal pyramid is a 3D shape that combines the base of a hexagon with the six triangles on the sides of the hexagon to form a pyramid at the apex. These triangles, either isosceles or equilateral, are called faces. A hexagonal pyramid has 7 angles, 7 faces, and 12 sides.
2. What is the formula for the volume of any hexagonal pyramid?
The formula for calculating the volume of a hexagonal pyramid is: Volume of hexagonal pyramid = (a. b. h) cubic units, where a is the apex of the pyramid, b is the base, and h is the height.
3. What is the formula for the surface area of a hexagonal pyramid?
The formula for the surface area of a hexagonal pyramid is: Surface area of a hexagonal pyramid = (3ab + 3bs) square units, where a is the apex of the pyramid, b is the base, and s is the height of the slope of the pyramid.
FAQs (Frequently Asked Questions)
1. What is the formula for the volume of a Hexagonal Pyramid Formula containing an equilateral triangle?
If the area of the hexagonal pyramid is equilateral and no maxim is mentioned, use the following formula to calculate the volume of the hexagonal pyramid.
Volume of hexagonal pyramid = (√3/2) × a2 × h cubic units, where a is the side of the base and h is the height of the hexagonal pyramid.
2. What is the formula for finding the base of a Hexagonal Pyramid Formula?
The formula for finding the base area of a hexagonal pyramid is Base area of hexagonal pyramid = 3ab square units, where a is the apex of the pyramid and b is the length of the base.
3. What is a hexagonal pyramid mesh?
A hexagonal pyramid mesh consists of six triangles attached to the sides of a hexagonal base. There are 7 areas in total. If one flattens the pyramid, one can clearly see the 6 faces and base of the triangle.
4. Does a hexagonal pyramid have 12 sides?
Each pyramid has its own characteristics and properties. A hexagonal pyramid has 12 sides and a polygonal base.