Video: Finding the Volume of an Oblique Pentagonal Prism given Its Base Area and Height

Determine the volume of an oblique pentagonal prism with a base area of 55 square centimeters and a perpendicular height of 2.8 centimeters.

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Video Transcript

Determine the volume of an oblique pentagonal prism with a base area of 55 square centimeters and a perpendicular height of 2.8 centimeters.

When we say a prism is oblique, it means that the bases are not directly on top of each other. It means that the solids can look slanted. However, we find the volume of an oblique prism in a similar way that we find the volume for any solid. To find the volume, we need to multiply the area of the base times the height.

The uppercase 𝐵 represents the area of the base. But here’s the key when dealing with an oblique prism. The height must be the perpendicular distance between the two bases. The perpendicular height creates a right angle between the two bases. That’s the height we’re interested in. We’re told that in this oblique pentagonal prism, the area of the base is 55 square centimeters. That would be the space shaded in pink, which is 55 centimeters squared. We’re also given the value of the perpendicular height, which is 2.8 centimeters. This means we have enough information to find the volume.

The volume of this oblique prism will be equal to 55 centimeter squared times 2.8 centimeters. When we multiply 55 by 2.8, we get 154. Volume is measured in cube units. So the volume of this oblique prism is equal to 154 centimeters cubed, which is our final answer.

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