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Prism – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">PrismPrism – Definition, ExamplesTable of ContentsUnderstanding Prisms in Mathematics Definition of Prisms

A prism is a solid three-dimensional shape that has flat faces, straight edges, and sharp corners. It has two identical faces called bases, which can be any polygon shape. The prism gets its name from the shape of these bases—for example, a prism with triangular bases is called a triangular prism. The remaining faces that connect the bases are called lateral faces, which are always parallelograms. Some key elements of a prism include edges (straight lines connecting adjacent corners), vertices (corners where edges meet), and faces (flat surfaces surrounded by edges).

Prisms can be categorized in several ways. Based on the shape of their bases, common types include triangular, square, rectangular, pentagonal, and hexagonal prisms. A square prism is also known as a cube, while a rectangular prism is often called a cuboid. Prisms can also be classified as regular (having regular polygon bases) or irregular (having irregular polygon bases). Additionally, they can be right prisms (where the lateral edges are perpendicular to the bases) or oblique prisms (where the prism appears tilted and the lateral faces are parallelograms).

Examples of Prisms Example 1: Finding the Volume of a Prism with Given Height and Base Area Problem:

Calculate the volume of a prism with a height of 777 cm and an area of the base of 606060 cm².

Examples of Prisms

Step-by-step solution:

Step 1, Recall the formula for the volume of a prism. The formula is: Volume=Area of base×Height\text{Volume} = \text{Area of base} \times \text{Height}Volume=Area of base×Height

Step 2, Fill in the known values into the formula. We know that height = 777 cm and area of base = 606060 cm².

Step 3, Multiply the area of the base by the height to find the volume: Volume=60×7=420 cm3\text{Volume} = 60 \times 7 = 420 \text{ cm}^3Volume=60×7=420 cm3

Example 2: Calculating the Surface Area of a Prism Problem:

Calculate the surface area of a prism with a base area of 252525 cm², a base perimeter of 242424 cm, and a height of 101010 cm.

Examples of Prisms

Step-by-step solution:

Step 1, Remember the formula for the surface area of a prism: Surface Area=(2×Base Area)+(Base perimeter×Height)\text{Surface Area} = (2 \times \text{Base Area}) + (\text{Base perimeter} \times \text{Height})Surface Area=(2×Base Area)+(Base perimeter×Height)

Step 2, Fill in the known values into the formula. We have base area = 252525 cm², base perimeter = 242424 cm, and height = 101010 cm.

Step 3, Calculate the total surface area:

First find the area of both bases: 2×25=50 cm22 \times 25 = 50 \text{ cm}^22×25=50 cm2 Then find the area of all lateral faces: 24×10=240 cm224 \times 10 = 240 \text{ cm}^224×10=240 cm2 Finally, add these values together: 50+240=290 cm250 + 240 = 290 \text{ cm}^250+240=290 cm2 Example 3: Computing the Volume with Base Area and Length Problem:

Find out the volume of a prism with a base area of 252525 cm² and a height of 121212 cm.

Examples of Prisms

Step-by-step solution:

Step 1, Understand that for a prism, the length refers to the height. We use the formula: Volume=Area of base×Height\text{Volume} = \text{Area of base} \times \text{Height}Volume=Area of base×Height

Step 2, Fill in the known values. In this case, height = 121212 cm and area of base = 252525 cm².

Step 3, Calculate the volume by multiplying these values: Volume=25×12=300 cm3\text{Volume} = 25 \times 12 = 300 \text{ cm}^3Volume=25×12=300 cm3

Comments(6)CCricketPlayerRyanNovember 6, 2025I've used this prism def for my kid's study. It's super clear, helped them grasp types & calcs. Great resource!

NNatureLover25September 17, 2025I used the Prism definition and examples here to help my kids with their geometry homework—it’s super clear and easy to follow! The step-by-step solutions were a lifesaver. Thanks for making math less intimidating!

MCMs. CarterSeptember 10, 2025I’ve used the prism definition and examples here to help my kids with their math homework—it’s super clear and the step-by-step solutions make tough concepts easy to understand. Great resource!

NNatureLover87August 27, 2025This page on prisms was super helpful for my 5th grader’s geometry homework! The examples are clear, and the step-by-step solutions made it easy for her to understand volume and surface area. Thanks for making math less stressful!

NNatureLover25August 20, 2025This page really helped my son understand prisms! The clear examples and step-by-step solutions made it so easy to explain volume and surface area. We even used it for his homework! Thanks!

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