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.
Hexagonal Pyramid
How many faces,edges and vertices does a hexagonal pyramid have?
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.
Formulas
Volume
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 cm3
Surface Area
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 (LSA)
∴ 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 in2
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 cm2 Total Surface Area (TSA) = 3ab + LSA, here a = 2.59 cm, b = 3 cm, LSA = 63 cm2 ∴ TSA = 3 × 7.79 × 9 + 63 = 273.33 cm2
