A hexagonal pyramid is a different kind that pyramid the exists. A hexagonal pyramid has actually the base in the form of a hexagon in addition to isosceles triangles as the faces that integrate the pyramid together at the apex. Let united state learn an ext about the principle of a hexagonal pyramid in this article.
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|1.||Hexagonal Pyramid Definition|
|2.||Hexagonal Pyramid Properties|
|3.||Volume the a Hexagonal Pyramid|
|4.||Surface Area of a Hexagonal Pyramid|
|5.||Hexagonal Pyramid Net|
|6.||FAQs top top Hexagonal Pyramid|
A hexagonal pyramid is a 3D shame pyramid that has actually the basic shaped like a hexagon in addition to the political parties or encounters in the shape of isosceles triangle that kind the hexagonal pyramid at the apex or the peak of the pyramid. A hexagonal pyramid has a base through 6 sides together with 6 isosceles triangular lateral faces. The other name because that a hexagonal pyramid is Heptahedron. A hexagonal pyramid is composed of 7 faces, 12 edges, and 7 vertices. Picture of a hexagonal pyramid is given listed below for her reference.
Hexagonal Pyramid Properties
Just like any other pyramid, a hexagonal pyramid additionally has unique properties that differentiate it indigenous the various other pyramids. Let's see what space those properties:There room 7 vertices in total in a hexagonal pyramid where 6 is at the base of the pyramid and also one at the topIn total, a hexagonal pyramid has 7 faces, one because that each side of the triangle in addition to one base
Volume of Hexagonal Pyramid
To calculate the volume the a hexagonal pyramid, we require to know three significant aspects the the hexagonal pyramid i.e. The apothem i m sorry is measured indigenous the center of the basic to any suggest on the side of the base, 2nd is the length of the base, and 3rd is the height which is the height of the pyramid native the apex come the base. Hence, the formula to calculation the hexagonal pyramid volume is:
Volume the Hexagonal Pyramid = (abh) cubic units
Where,a is the apothem of the pyramidb is the baseh is the height
When the apothem of the hexagonal pyramid is no mentioned and also when the triangles are equilateral triangles, we deserve to use another different formula i beg your pardon is:
Volume of hexagonal Pyramid = (√3/2) × a2 × h cubic units, whereby a is the side of the base and also h is the elevation of the hexagonal pyramid
Surface Area of a Hexagonal Pyramid
Before us calculate the surface area that a hexagonal pyramid, we also need to understand its base. The surface area the the hexagonal pyramid deserve to be calculated once we have the slant elevation of the pyramid i beg your pardon is the elevation from the apex to any point on the boundary of the base of the pyramid. Hence, let us see both the formula of the hexagonal pyramid - base area and also surface area.
Base Area that Hexagonal Pyramid = 3ab square units
Surface Area that Hexagonal Pyramid = (3ab + 3bs) square units
Where,a is the apothem that the pyramidb is the bases is the slant height of the pyramid
Hexagonal Pyramid Net
A hexagonal pyramid is composed of 7 faces, 7 vertices, and 12 edges. The net of the hexagonal pyramid is developed with a hexagon-shaped base consists of 6 sides follow me which 6 triangles are developed by connecting the edges of the base. These triangles are dubbed the lateral faces of the pyramid. When the pyramid is flattened, the 6 triangles and also one hexagon base room seen i.e 6 faces and also one face in the base. Check out the below image together reference:
Hexagonal Pyramid related Topics
Listed below are couple of interesting topics the are related to the concept of a hexagonal pyramid. Have actually a look!
Examples ~ above Hexagonal Pyramid
Example 1: Find the volume that a hexagonal pyramid with apothem size of 6 units, base size as 9 units, and height together 15 units.
Solution: provided is, a = 6, b = 9, and h = 15. Let's location the values in the formula the the volume.
Hexagonal Pyramid Volume = abh cubic units
Volume = 6 × 9 × 15
Volume = 810 units3
Therefore, the volume that the offered hexagonal pyramid is 810 units3.
Example 2: What would be the basic area and the surface ar area that a hexagonal pyramid, if it has actually an apothem size of 4 units, base length as 9 units, and slant elevation as 14 units?
Solution: given is a = 4, b = 9, and also s = 14
Let's calculate the basic area of the hexagonal pyramid first,
Base Area = 3ab square units
Base Area = 3 × 4 × 9
Base Area = 108 units2
Next, let's calculate the surface area the the hexagonal pyramid,
Surface Area = 3ab + 3bs square units
Surface Area = 3 × 4 × 9 + 3 × 9 × 14
Surface Area = 108 + 378
Surface Area = 486 units2
Therefore, the surface ar area of the pyramid is 486 units2 and the basic area is 108 units2.
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FAQs on Hexagonal Pyramid
What is a Hexagonal Pyramid?
A hexagonal pyramid is a 3D shape with the basic of a hexagon merged with 6 triangles versus the sides of a hexagon erected to form a pyramid at its apex. These triangles can be one of two people an isosceles triangle or an it is intended triangle and they are called lateral faces. A hexagonal pyramid consists of 7 vertices, 7 faces, and 12 edges.
What is the Formula to discover the Volume that a Hexagonal Pyramid?
The formula to calculate the volume of a hexagonal pyramid is, Volume of Hexagonal Pyramid = (abh) cubic units, where a is the apothem that the pyramid, b is the base, and also h is the height.
What is the Formula to uncover the surface Area that a Hexagonal Pyramid?
The formula to uncover the surface area of a hexagonal pyramid is, surface ar Area the Hexagonal Pyramid = (3ab + 3bs) square units, wherein a is the apothem of the pyramid, b is the base, and also s is the slant height of the pyramid.
What is the Formula to discover the Volume of Hexagonal Pyramid with Equilateral Triangles?
When the faces of the hexagonal pyramid room equilateral triangles and also the apothem is not mentioned, the complying with formula is supplied to calculate the volume of a hexagonal pyramid.
Volume the hexagonal Pyramid = (√3/2) × a2 × h cubic units, wherein a is the next of the base and also h is the elevation of the hexagonal pyramid.
What is the Formula to uncover the base Area the the Hexagonal Pyramid?
The formula to discover the basic area of a hexagonal pyramid is, base Area the Hexagonal Pyramid = 3ab square units, whereby a is the apothem the the pyramid and b is the base length.
What is the network of a Hexagonal Pyramid?
The net of a hexagonal pyramid is formed with 6 triangle attached follow me the sides of the hexagon-shaped base. There are 7 deals with in complete i.e. 6 encounters of the triangle and one basic which is seen clearly when the pyramid is flattened.
See more: What Does A Cursive F Look Like, Letter F: Cursive Script
Does a Hexagonal Pyramid have actually 12 Edges?
Every pyramid has actually its very own characteristics and properties that are distinctive to them. A hexagonal pyramid does have 12 edges through the basic shaped favor a polygon.