A right hexagonal prism with height 5cm and base edge 6cm

Question

Find lateral area, total area, and volume 

Answer 1

Hi Dez,

 

There are probably formulas but I will show you how to find the answer without using formulas.

 

The base is a hexagon and it is a regular hexagon. Therefore, all sides and all angles are equal.

The measure of one interior angle of a hexagon is 120 degrees. It is composed of six equilateral triangles. Therefore, the area of one base is the sum of 6 equilateral triangles with side length 6 cm.

The area of an equilateral triangle is a^2sqrt(3)/4  where a is the side length.

We are given a=6 cm, so the area of one base is

6*6^2sqrt(3)/4 = 54sqrt(3) cm^2

Since we have two bases, 2*54sqrt(3) = 108√3 cm^2 is the total area of the bases.

The lateral surfaces are rectangles with width 5 and height 6 cm. There are six of them, so

lateral surface area = 6*(6*5) = 180 cm^2

total area = base area + lateral surface area

= 180 + 108√3

= 180 + 187

= 367 cm^2 (rounded to the nearest whole number)

Volume is equal to base area*height. So,

V = 54√3*5

= 270√3

= 468 cm^3 (rounded to the nearest whole number)

 

I hope this all makes sense!

You can check to see if the answers I got are true using the formulas you can find online. I did.