A right hexagonal prism has a height of 9 centimeters, and each base edge is 4 centimeters.
Unfortunately, we do not know if the base is a regular polygon. Notice that even if every edge of a hexagon is the same, it is not enough for it to be regular. For example, here are two equilateral hexagons.
The hexagon on the left is regular, and the one on the right is not. From now on we will assume that the base of the prism is a regular hexagon. Otherwise, we have too little data to solve the exercise. Let's analyze the base of the prism and divide it into 6 equilateral triangles.
We are asked to find the surface area of the hexagonal prism, S. It is equal to S=L+2B, where L is its lateral area and B is its base area.
Base Area
Since the base consists of 6 equilateral triangles, we will use the formula for the area of a equilateral triangle A_(△), with a side length of s.
The area of the base is about 41.57 square centimeters.
Lateral Area
Now, let's find the lateral area L. It is equal to L= P h, where P is the perimeter of the base and h is the height of the prism. This tells us that h= 9 cm. Since the base is an equilateral hexagon, its perimeter is P=6* 4= 24 cm. Now, let's calculate L!
We calculated that the base area is about B=41.57 square centimeters and the lateral area is L=216 square centimeters. Now, let's find the surface area of the given prism.
