SOLUTION: In the regular pentagonal pyramid, each lateral edge measures 11 in., and each base edge measures 7 in. The apothem of the base measures 4.8 in. Find the lateral area (in square

Algebra ->  Formulas -> SOLUTION: In the regular pentagonal pyramid, each lateral edge measures 11 in., and each base edge measures 7 in. The apothem of the base measures 4.8 in. Find the lateral area (in square      Log On


   

Question 1194251: In the regular pentagonal pyramid, each lateral edge measures 11 in., and each base edge measures 7 in. The apothem of the base measures 4.8 in.
Find the lateral area (in square inches) of the pyramid.
Find the total area (in square inches) of the pyramid.
Answer by math_tutor2020(3817) About Me  (Show Source):
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n = number of sides in the base = 5
x = length of each side = 7

A = area of a regular polygon with n sides
A = (perimeter)*(apothem)/2
A = (x*n)*(apothem)/2
A = (7*5)*(4.8)/2
A = 84 square inches

The pentagonal floor has an area of 84 square inches.

Each lateral edge measures 11 inches, which I'm assuming is the slant height of each triangular face.
This would mean the triangles have a base of 7 and height of 11.
area = base*height/2
area = 7*11/2
area = 38.5
Each triangular face has an area of 38.5 square inches.
Five such identical faces gives a lateral area of 5*38.5 = 192.5 square inches.

Add this to the base pentagonal area to get the total surface area
84+192.5 = 276.5


Answers:
Lateral Area = 192.5 square inches
Total Surface Area = 276.5 square inches