Table of Contents

Last modified on September 6th, 2022

A hexagonal pyramid is a solid with a hexagonal base bounded by six lateral faces meeting at a common point, known as the apex. The lateral faces are in shape of isosceles triangles.

**How many faces,**

A hexagonal pyramid has 7 faces, 7 vertices, and 12 edges. Since it has 7 flat faces, a hexagonal pyramid is also called a heptahedron.

Like all other polyhedrons, we can calculate the surface area and the volume of a hexagonal pyramid.

The formula is:

**Volume ( V) =** ${\dfrac{\sqrt{3}}{2}b^{2}h}$, here b = base, h = height

Let us solve an example to understand the concept better.

**Find the volume of a hexagonal pyramid with a base of 7 cm, and a height of 10 cm.**

Solution:

As we know,

Volume (*V*) = ${\dfrac{\sqrt{3}}{2}b^{2}h}$, here b = 7 cm, h = 10 cm

∴*V* = ${\dfrac{\sqrt{3}}{2}\times 7^{2}\times 10}$

= 424.35 cm^{3}

We can calculate 2 types of surface areas: (1) Lateral Surface Area (*LSA*), and (2) Total Surface Area (*TSA*)

The formula is:

**Surface Area (SA) = 3ab + 3bs, **here a = apothem, b = base, s = slant height,

Also, ** 3bs** = lateral surface area (

∴ *SA* = **3ab****+ LSA**

Let us solve some examples to understand the concept better.

**Find the surface area of a hexagonal pyramid with a base of 9 in, an apothem of 7.79 in, and a slant height of 16 in.**

Solution:

As we know,

Total Surface Area (*TSA*) = 3ab + 3bs, here a = 7.79 in, b = 9 in, s = 16 in

∴ *TSA* = 3 × 7.79 × 9 + 3 × 9 × 16

= 642.33 in^{2}

**Find the lateral and total surface areas of a hexagonal pyramid with a base of 3 cm, an apothem of 2.59 cm, and a slant height of 7 cm.**

Solution:

As we know,

Lateral Surface Area (*LSA*) = 3bs, here b = 3 cm, s = 7 cm

∴ *LSA* = 3 × 3 × 7

= 63 cm^{2}

Total Surface Area (*TSA*) = 3ab + *LSA,* here a = 2.59 cm, b = 3 cm, *LSA* = 63 cm^{2}

∴ *TSA* = 3 × 7.79 × 9 + 63

= 273.33 cm^{2}

Last modified on September 6th, 2022