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High School Geometry: Homework Help Resource13 chapters | 142 lessons

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Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, learn what prisms are and what makes square prisms unique. Included are a few examples of square prisms and the qualities that make up these three dimensional objects.

Prisms make up many everyday objects, but what makes them stand out? A **prism** is a three dimensional solid object with flat sides and bases that are the same. For example, a tissue box is a prism because it has opposite bases that are the same, and flat sides that are parallelograms. Dice are prisms; the bases are flat faces and in this example, they are square. Joined together, they make the enclosed three-dimensional shape shown here:

A prism has two parallel **faces**, or the distinct flat surfaces or slides of a solid. These faces are called **bases**, and they are used to name the type of prism. Looking around a classroom, kitchen or office, prisms with square, rectangular, and triangular faces can be quite easy to spot.

Since there are many different shapes that can serve as the base of a prism, there are many types of prisms that can be made. Prisms are named for the shape of their bases, so a **square prism** is simply a prism that has squares as its bases. Think again about dice; they are enclosed three-dimensional shapes, based on two *squares*.

In fact, regular dice are cubed, all the faces are square. So cubes are a square prism no matter how they are looked at!

A common real-world example of a cube is the famous Rubik's Cube. When identifying a square prism, all the faces don't have to be squares. Remember, as long as the shapes have two square faces, meaning it's bases are squares, it's a square prism.

For example:

Although this box is rectangular, its front and back are squares, making this shape a square prism. Think of all the different sizes and shapes of cardboard boxes; many are square prisms, because their bases are squares and their side faces are parallelograms. Moving boxes are sometimes square prisms.

Although the sides of this box are rectangular, the top and bottom (if the box was closed) are both square, so this box is a square prism. Picture a pizza box; is it a three dimensional object? Does it have bases that are squares? Are the other side faces parallelograms? The answer is yes to all of these questions. A pizza box is a square prism.

A **prism** is simply two bases that are the same, joined together by flat sides to form an enclosed three-dimensional shape. By definition, a **square prism** is a three-dimensional shape with two square bases and flat sides. Therefore, all square prisms consist of at least two squares, even if not all the sides are squares, as long as the bases are square, there is a square prism.

Cubes are a common example of square prisms. However, a cube has also sides that are square. Square prisms can be identified in many household objects; cardboard boxes are prisms, and if they have square bases, they can be identified as square prisms.

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High School Geometry: Homework Help Resource13 chapters | 142 lessons

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