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3 years ago

A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.

Mathematics

2 answers:

denpristay [2]3 years ago

7 0

The area is given by:
A = Ab + Al
Where,
Ab: base area
Al: lateral area
The area of the base is:
Ab = (3/2) * (L ^ 2) * (root (3))
Where,
L: side of the hexagon.
Substituting we have:
Ab = (3/2) * (4 ^ 2) * (root (3))
Ab = (3/2) * (16) * (root (3))
Ab = 24raiz (3)
The lateral area is:
Al = (6) * (1/2) * (b) * (h)
Where,
b: base of the triangle
h: height of the triangle
Substituting we have:
Al = (6) * (1/2) * (4) * (6)
Al = 72
The total area is:
A = 24raiz (3) + 72
Answer:
A = 24raiz (3) + 72

Shalnov [3]3 years ago

3 0

The answer would be A = 24raiz (3) + 72
Formula:
A = Ab + Al Where, Ab= base area Al= lateral area

The base are:
Ab = (3/2) * (L ^ 2) * (root (3)) Where, L= side of the hexagon.

Substitute:
Ab = (3/2) * (4 ^ 2) * (root (3)) Ab = (3/2) * (16) * (root (3)) Ab = 24raiz (3)

The lateral area is: Al = (6) * (1/2) * (b) * (h) Where, b=base of the triangle h= height of the triangle
Substitute: Al = (6) * (1/2) * (4) * (6) Al = 72 The total area is: A = 24raiz (3) + 72

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