The lateral faces (triangles) of a pyramid meet at a common point known as the vertex. A pyramid’s name is derived from the name of the polygon that defines its base. A square pyramid, a rectangular pyramid, a triangular pyramid, a pentagonal pyramid, a hexagonal pyramid, and so on are examples of pyramids.
Let’s discuss the hexagonal pyramid in details,
A hexagonal pyramid is a pyramid with a hexagonal base and six isosceles triangular faces that intersect at a point in geometry (the apex). It is self-dual, just like any other pyramid. C6v symmetry is found in a right hexagonal pyramid with a regular hexagon base. A right regular pyramid has a regular polygon as its base and an apex that is “above” the centre of the base, creating a right triangle with the apex, the centre of the base, and every other vertex. It is also known as Heptahydron.
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Hexagonal Pyramid Formula
A pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height (h) is a special case of the formula for a regular n-gonal pyramid with n = 6.
The formula of the base area of a hexagonal pyramid is,
b = 3 x a x b
where a is the length of a side of the base. The hexagon volume formula is,
V = a x b x h
and the hexagonal surface area formula is,
S = (3 x a x b) + (3 x b x s)
Where,
a is apothem length of the pyramid.
b is the base length of the pyramid.
s is the slant height of the pyramid.
h is the height of the pyramid.
Examples for Hexagonal Pyramid
Ex.1. Find The Base Area, The Surface Area of Hexagon And Volume of A Hexagonal Pyramid of Apothem Length 3 Cm, Base Length 6 Cm, Height 8 Cm And Slant Height 14 Cm?
Answer:
Given,
a = 3 cm
b = 6 cm
h = 8 cm
s = 14 cm
Base area of a hexagonal pyramid
b = 3 x a x b
= 3 × 3 cm × 6 cm
= 54 cm2
Surface area of hexagon pyramid
S = (3 x a x b) + (3 x b x s)
= (3 × 3 cm × 6 cm) + (3 × 6 cm × 14 cm)
= 54 cm2 + 252 cm2
= 304 cm2
Hexagon volume formula is,
V = a x b x h
= 3 cm × 6 cm × 8 cm
= 144 cm3
Hence, the Base area of a hexagonal pyramid is 54 cm2
The surface area of hexagon pyramid is 304 cm2
The volume of a hexagonal pyramid is 144 cm3
Ex.2. Find The Height of A Hexagonal Pyramid When The Volume (V) of A Pyramid is 169 cm3, the base (b) length of the pyramid is 9cm and the apothem (a) length of the pyramid is 7cm?
Answer:
Given,
a = 7 cm
b = 9 cm
h = ?
V = 169 cm3
Now, use the volume formula to find the height of a hexagonal pyramid.
V = a x b x h
169 = 7 x 9 x h
Hence,
h = 169/63
h = 2.68 cm
The height of a hexagonal pyramid is 2.68cm.