The lateral area of a right prism is equal to L= P h, where P is a perimeter of the base and h is the height of the prism.
216 square meters
A right hexagonal prism has a height of 12 meters and each base edge is 3 meters. Let's rotate the prism so that the hexagons are horizontal.
We are asked to find the lateral area of the prism L. It is equal to L= P h, where P is a perimeter of the base and h is the height of the prism. This tells us that h= 12 meters. Since the base is an equilateral hexagon, its perimeter is P=6* 3= 18 meters. Now, let's calculate L!
The lateral area is 216 square meters.
<ebox title="The Shape of the Base" type="Extra">
We know that the base is a equilateral hexagon. Notice that even if every edge of a hexagon is the same, it is not enough for it to be regular. Below we present two equilateral hexagons.
The hexagon on the left is regular, and the one on the rightis not.
</ebox>
