106. (14 points) Find the lateral area, surface area, and volume of the pentagonal pyramid.(a) Apothem of the base, a18 in.16 in.12.6 in.(b) Perimeter of the base, p(c) Area of the base, B(d) Lateral area of the solid, L(e) Surface area of the solid, T(f) Volume of the solid, V

Answered: 14 points) Find the lateral area,…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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6. (14 points) Find the lateral area, surface area, and volume of the pentagonal pyramid.
(a) Apothem of the base, a
18 in.
16 in.
12.6 in.
(b) Perimeter of the base, p
(c) Area of the base, B
(d) Lateral area of the solid, L
(e) Surface area of the solid, T
(f) Volume of the solid, V

Expert Solution

Step 1

Definition used -

Apothem for a polygon having n sides -

$a = \frac{s}{2 \tan (\frac{180}{n})}$

Perimeter = Sum of the length of sides

Area of pentagon $A = \frac{1}{2} a n s$

Here s= side length of pentagon

n = number of sides

a = length of apothem

Step 2

GIven -

a) Here side length s= 12.6

$a = \frac{12.6}{2 \tan (\frac{180}{5})} = 8.67$

b) Perimeter of the base $P = 5 \times 12.6 = 63 i n .$

c) Area of base $B = \frac{1}{2} a n s$

$B = \frac{1}{2} \times 8.67 \times 5 \times 12.6$

$= 273.105 i n^{2}$

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14 points) Find the lateral area, surface area, and volume of the pentagonal pyramid. (a) Apothem of the base, a 18 in. 16 in. 12.6 in.