What is the volume, lateral area, and total area of a right regular
hexagonal pyramid with base edges of 16 ft. and an altitude of 20 ft.?

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Request for Question Clarification by politicalguru-ga on 26 May 2004 03:53 PDT

Do you need the formula that helps to solve such questions?

Equations required:
http://www.drking.plus.com/hexagons/misc/area.html
http://mathworld.wolfram.com/HexagonalPyramid.html

The surface area (SA) of the hexagonal pyramid is:

SA = 1.5*(a²sqrt(3) + sqrt(3a² + 4h²))

Subsititute a = 16 and h = 20 into the above equation and you get the
answer 738.1 square feet.

The lateral area of a hexagonal pyramid is the total surface area
minus the base area (as the lateral area is the area touching the top
and base, ie the sides of the shape).

The base of the hexagonal is given by the following formula:

Base = 1.5*sqrt(3)*a²

Substituting a into this equation gives a base area of 665.1 square feet.

Therefore the lateral area is SA-Base = 73 square feet.

The volume of the hexagonal pyramid is given by the formula:

Vol = 0.5*sqrt(3) * h * a²

By substituting in the values for h and a you get a volume of 4434.1 cubic feet.

The answers given here are accurate to 1 decimal place, you may also
want to run them through a calculator to ensure their accuracy.  I was
doing these longhand on a piece of paper!

If you have any more questions on hexagonal pyramids or would like
further clarification please ask before rating the question.  I am
here to help you!

Thank you that cleared things up for me.

These sites might help:

http://mathworld.wolfram.com/HexagonalPyramid.html
http://mathworld.wolfram.com/Hexagon.html
http://www.csun.edu/~math095/schedule/notes/geo/Solids/Solids.html

There's never any need to do these calculations on paper as long as
you have the Google Calculator handy!

://www.google.com/help/features.html#calculator