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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

The figure below is a regular hexagonal pyramid.

a) Find the lateral area L of the pyramid.

b) Find the total area T of the pyramid.

c) Find the volume V of the pyramid.

To determine

(a)

To find:

The lateral area of the pyramid.

Explanation

Given:

A regular hexagonal pyramid as below,

Base side is 6ft and altitude h=8ft.

Properties used:

A pyramid is made by connecting a base to an apex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles.

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.

The lateral area L of a regular pyramid with slant height of length l and perimeter P of the base is given by

L=12lP.

In a regular pyramid, the lengths of the apothem a of the base, the altitude h, and the slant height l satisfy the Pythagorean Theorem; that is, l2=a2+h2.

The perimeter of the square is four times the side.

Calculation:

From the given figure

The sides of the square base measure 6ft each and that altitude measures 8ft i.e. h=8ft.

Since, the side of base is 6ft and the angle at the center for each base is 60° which is bisected by the perpendicular so the apothem in the right-angled triangle is given by the perpendicular side i.e. a=side2tan30°

To determine

(b)

To find:

The total area of the pyramid.

To determine

(c)

To find:

The volume of the pyramid.

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