Volume (V) of a prism is calculated using the formula: V = Base Area × Height, where the base area is the area of one of the bases.

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In this article, we will learn about all the details related to Prism including the shape of the prism, cross-section of a prism, examples of the prism, various types of Prism, the difference between a pyramid and a prism, etc.

A cross-section forms when a 3D object is sliced by a plane along its axis. In simpler terms, you can think of it as cutting a 3D object with a flat plane to create a different shape.

Volume is how much space a prism takes up. To find the volume of a prism, simply multiply the base area by its height. The volume of a prism is represented as V = B × H. The base area is measured in square units (units²), and the height is in linear units (units), so the unit of volume is given as units³.

A prism in maths is a part of the polyhedron family and has identical polygons at the top and bottom. The other faces of a prism are called lateral faces and they have the same shape all along their length, but it doesn't have curved faces. Prisms are named based on their cross-sections.

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There are seven types of prisms we have discussed earlier, and each type has different base shapes. Therefore, the formulas for finding the surface area of the prism vary depending on the specific type of prism.

An oblique prism seems slanted because its flat ends aren't perfectly aligned. The sides form parallelograms, creating an inclined shape. This occurs due to the prism's construction. It's this structure that causes the visual effect of tilting when observed from certain angles.

Lateral area of a prism is the sum of the areas of its lateral faces and is calculated using the formula: LA = Perimeter of Base × Height.

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Example 1: Find the volume of a rectangular prism with a length of 8 units, a width of 4 units, and a height of 6 units.

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Q2. Calculate the total surface area of a pentagonal prism with a base side length of 6 centimeters and a height of 10 centimeters.

A prism has two identical bases and rectangular sides, while a pyramid has one base and triangular sides that meet at a common vertex.

Prisms are named based on the shape of their cross-sections, which means the shape you get when you cut them. The diffferent types of Prism based on the shape of base are:

A right prism is a solid shape with flat ends that align perfectly and creates rectangular bases. Its side faces are also rectangular, tha gives a consistent, upright structure. This geometric structure plays a crucial role in various mathematical concepts and practical applications.

A prism is a three-dimensional solid with two identical, parallel bases and rectangular sides connecting corresponding vertices of the bases.

If a plane parallel to its base intersects a prism, the resulting cross-section will match the shape of the base. For instance, when a plane cuts through a square pyramid in the same direction as its base, the cross-section will also be a square. This means the shape after the cut is the same as the starting shape.

In contrast, an irregular prism features a base in the shape of an irregular polygon, where the sides and angles are not equal. This leads to a prism with non-uniform and asymmetric characteristics. The faces and edges exhibit a less predictable arrangement, making geometric calculations and analysis more complex due to the lack of symmetry.

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A prism is a 3D shape with flat, identical faces at its two ends. The other faces are flat as well. The name of a prism depends on the shape of its base. There are different types of prisms named after their base shapes.

Some prisms, like oblique prisms, may have slant heights. The slant height is the distance between the vertices of the bases along the lateral faces.

Lateral Area of a prism is the sum of the areas of all its side faces. On the other hand, the Total Surface Area of a prism is the sum of its lateral area and the area of its bottom and top faces.

Examples include rectangular prisms (like boxes), triangular prisms (like certain roof shapes), and more complex prisms in architecture.

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A prism and a pyramid are distinct three-dimensional geometric shapes. The key difference lies in their base configuration. A prism has two identical parallel bases, which are typically polygons, and its sides are rectangular.

Prisms is a 3D shapes that have two flat ends and rectangular side faces. In everyday life, we see prisms in things like buildings and optical devices like cameras and glasses. They're practical and important in many ways.

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A regular prism is characterized by a base that takes the form of a regular polygon, which means all its sides and angles are equal. This results in a prism with uniform and symmetric properties. The faces and edges are organized in a structured and predictable manner, making calculations and geometric analysis more straightforward.

For the total surface area of a prism, there are two methods to calculate: by adding two times the base area to the lateral surface area, or by adding two times the base area to the product of base perimeter and height.

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A prism has mainly two formulas, one is the surface area of the prism and another one is volume of prism. Let's learn them in detail.

Q4. Find the total surface area of a trapezoidal prism with bases measuring 5 and 8 centimeters, and a height of 10 centimeters.

In contrast, a pyramid has a single base, often a polygon, and triangular sides that converge at a common point called the apex.

Prisms can be classified by the shape of their bases, such as rectangular prisms, triangular prisms, pentagonal prisms, etc.

Prism is a solid shape consisting of two identical ends (such as triangles, squares, rectangles, etc.), having flat faces or surfaces and maintaining a uniform cross-section across its length. Consequently, a prism can have square, rectangular, pentagonal, and other polygonal shapes but cannot take on a circular form.