Question

Find the lateral area and the surface area of the regular hexagonal pyramid.


Question 8 options:

lateral area = 385.1 cm2; surface area = 805 cm2

lateral area = 231.6 cm2; surface area = 441 cm2

lateral area = 210 cm2; surface area = 325.5 cm2

lateral area = 21.8 cm2; surface area = 231.2 cm2

Answer 1

Answer:

Part 1) The lateral area is $LA=210\ cm^2$

Part 2) The surface area is $SA=325.5\ cm^2$

so

lateral area = 210 cm2; surface area = 325.5 cm2

Step-by-step explanation:

Part 1) Find the lateral area of the regular hexagonal pyramid

The lateral area is equal to the area of its six triangular faces

so

$LA=6[\frac{1}{2}bh]$

we have

$b=7\ cm\\h=10\ cm$

substitute

$LA=6[\frac{1}{2}(7)(10)]$

$LA=210\ cm^2$

Part 2) Find the surface area of the regular hexagonal pyramid

The surface area is equal to the lateral area plus the area of the hexagonal base

so

$SA=LA+B$

where

B is the area of the hexagonal base

Find the area of the hexagonal base

The area of the regular hexagon is equal to the area of six equilateral triangles

$B=6[\frac{1}{2}(b)(h)]$

we have

$b=7\ cm\\h=5.5\ cm$

substitute

$B=6[\frac{1}{2}(7)(5.5)]$

$B=115.5\ cm^2$

The surface area is equal to

$SA=210+115.5=325.5\ cm^2$

Answer 2

Answer:

lateral area = 210 cm2; surface area = 325.5 cm2 is correct.

Step-by-step explanation: