[Maths Class Notes] on Hexagonal Pyramid Formula Pdf for Exam

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.