## Hexagonal Pyramid

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 cm^{2}

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 cm^{2} + 252 cm^{2}

= 304 cm^{2}

Hexagon volume formula is,

V = a x b x h

= 3 cm × 6 cm × 8 cm

= 144 cm^{3}

Hence, the Base area of a hexagonal pyramid is 54 cm^{2}

The surface area of hexagon pyramid is 304 cm^{2}

The volume of a hexagonal pyramid is 144 cm^{3}

Ex.2. Find The Height of A Hexagonal Pyramid When The Volume (V) of A Pyramid is 169 cm^{3}, 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 cm^{3}

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.

1. How to Make Hexagonal Pyramid Out of Cardboard?

Answer: On a piece of cardboard, draw the template.

To create a hexagonal based prism out of cardboard, begin by copied the prism's template into paper or cardboard.

Reduce the size of the number. Using scissors, cut out the prism design.

Fold the cutout in two.

Glue the cut-out in position.

2. What is The Volume of This Pyramid?

Answer: The general formula for calculating the volume of a pyramid is: volume of a pyramid = 1/3 base area height.

Where Ab is the area of the polygonal base and h is the pyramid's height.

3. Why Pyramid is a Triangle?

Answer: A pyramid's base can be a triangle, a cube, a rectangle, or some other form with multiple sides.

A triangle is formed by each side of a pyramid (the base edge and the apex).