Question

A regular hexagonal prism has a height of 7 cm and base edge length of 4 cm. Identify its lateral area and surface area. HELP ASAP

Answer 1

Answer:

Lateral Surface Area = 168 $cm^2$

Total Surface Area = 209.57 $cm^2$

Step-by-step explanation:

Given:

There is a regular hexagonal prism with

Height, h = 7 cm

Base edge length, a = 4 cm

To find:

Lateral surface area and total surface area = ?

Solution:

Formula for lateral surface area is given as:

$LSA = \text{Perimeter of Base}\times Height$

Perimeter of a hexagon is given as:

$P = 6 \times Edge\ Length\\\Rightarrow P = 6\times 4=24\ cm$

Now, LSA = 24 $\times$ 7 = 168 $cm^2$

Total Surface area of prism is given by the formula:

$TSA = LSA + B$

where B is the area of base.

Base is a regular hexagon, formula for area of a regular hexagon is given by:

$B =6\times \dfrac{\sqrt3}4\times Edge^2\\\Rightarrow B =6\times \dfrac{\sqrt3}4\times 4^2 = 24\sqrt3\ cm^2\\\Rightarrow B = 41.57 cm^2$

So, Total Surface Area = 168 + 41.57 = 209.57$cm^2$

So, answer is :

Lateral Surface Area = 168 $cm^2$

Total Surface Area = 209.57 $cm^2$