Answer:
Lateral Surface Area = 168 [tex]cm^2[/tex]
Total Surface Area = 209.57 [tex]cm^2[/tex]
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:
[tex]LSA = \text{Perimeter of Base}\times Height[/tex]
Perimeter of a hexagon is given as:
[tex]P = 6 \times Edge\ Length\\\Rightarrow P = 6\times 4=24\ cm[/tex]
Now, LSA = 24 [tex]\times[/tex] 7 = 168 [tex]cm^2[/tex]
Total Surface area of prism is given by the formula:
[tex]TSA = LSA + B[/tex]
where B is the area of base.
Base is a regular hexagon, formula for area of a regular hexagon is given by:
[tex]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[/tex]
So, Total Surface Area = 168 + 41.57 = 209.57[tex]cm^2[/tex]
So, answer is :
Lateral Surface Area = 168 [tex]cm^2[/tex]
Total Surface Area = 209.57 [tex]cm^2[/tex]
