Determine the volume of an oblique hexagonal prism, with a base area of 125 square centimeters and a perpendicular height of 125 centimeters.
In any oblique prism, the bases are not aligned when directly above the other. And the lateral faces are parallelograms. Just like the volume of any other solid, the volume of an oblique prism is equal to the area of the base times the height. If volume is equal to capital 𝐵 times ℎ, capital 𝐵 is the area of the base. The ℎ represents the perpendicular height. That’s the perpendicular distance between the two bases, which would be this distance on our sketch.
We’re given that the area of the base is 125 centimeters squared. And the perpendicular height is equal to 125 centimeters. To find the volume then, we multiply the area of the base, 125 centimeters squared, times the height, 125 centimeters. When we multiply 125 by 125, we get 15625. Since we’re dealing in volume, our units are cubed.
And we can say that the volume of this oblique hexagonal prism is 15625 centimeters cubed.