The cross-section of a prism is the shape obtained when you cut the prism through an axis. The cut is made in a straight line congruent to the bases in right angles. In other words, a prism has a cross-section exactly of the same shape and size throughout its length. For example, a triangular prism has a triangular cross-section end to end throughout its length.

Given, base area = 35 in2 and height = 6 in We know that, The volume of a prism (V) = Base area × Height Thus, V = 35 × 6 = 210 in3 Therefore, the volume of the triangular prism is 210 in3

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There are seven types of prisms we read above based on the shape of the bases. The bases of different types of prisms are different so are the formulas to determine the surface area of the prism. See the table below to understand this concept behind the surface area of various prisms:

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A prism is a three-dimensional solid with two identical bases. The total surface area of prisms can be found by adding 2 times the area of its base and its lateral surface area.

Example 2: What will be the surface area of the prism if the length, breadth, and height of the prism are 8 units, 6 units, and 4 units respectively?

A prism is classified on the basis of the type of polygon base it has. There are two types of prisms in this category named as:

If the base of the prism is in the shape of a regular polygon, the prism is a regular prism. Whereas, if the base of the prism is in the shape of an irregular polygon, the prism is an irregular prism.

The volume of a prism is defined as the total amount of space or vacuum a prism occupies. The volume of a prism is the product of the area of the base and height of the prism. Thus, the volume of a prism is represented as V = B × H where "V" is the volume, "B" is the base area, and "H" height of the prism. The base area is given in (units2) and the height of the prism is given in (units). Thus, the unit of volume of the prism is given as V = (units2) × (units) = units3. Look at the table below to understand the formula behind the volume of various prisms:

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The lateral surface area of prism = base perimeter × height The total surface area of a prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area or (2 × Base Area) + (Base perimeter × height).

Prisms are an important member of the polyhedron family. A prism has two identical faces on which they are named upon. It is a 3-dimensional shape and can be categorized on the following basis:

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Solution: Given information is length = 8 units, breadth = 6 units, and height = 4 units. With this information, it is clearly observable that the prism is a rectangular prism. Surface area of a prism = (2 × Base Area) + (Base perimeter × height) Base area = length × breadth = 48 units2 Base perimeter = 2 (l + b) = 28 units Height = 4 units Substituting the values of the base area, base perimeter, and height in the surface area formula we get, Surface area of prism = (2 × 48) + (28 × 4) = 208 units2 Therefore, the surface area of the prism is 208 units2

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A prism is a three-dimensional solid which has identical faces at both ends. The other faces are flats. A prism is named after its base. Therefore, there are different types of prisms named on the basis of the shape of their bases. Let us explore more about the world of prisms!

Before reading about various types of prisms let us understand on what basis types of prisms can be obtained. Prisms can be classified on the following basis:

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A right prism has two flat ends that are perfectly aligned whereas an oblique prism appears to be tilted and the two flat ends are not aligned. In a right prism, all the side faces are rectangles whereas the faces of the oblique prism are parallelograms.

The lateral area of a prism is the sum of the areas of all its lateral faces whereas the total surface area of a prism is the sum of its lateral area and area of its bases.

There are two types of areas we read about, first, the lateral surface area of the prism, and second, the total surface area of the prism. Let us learn in detail.

A prism is an important member of the polyhedron family that has congruent polygons at the base and top. The other faces of a prism are called lateral faces. It means that a prism does not have a curved face. A prism has the same cross-section all along its length. The prisms are named depending upon their cross-sections. A metallic nut is the best example to represent hexagonal prism, fish aquarium represents rectangular prism and many more such live appliances in our surroundings represent the prisms.

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There are two basic formulas we read in geometry about all the respective 3-dimensional shapes. The two formulas are the area of the shape and volume of the shape. Let us learn these two in the case of prisms.

A prism is a polyhedron that has the same cross-section along all its length. The volume of the prisms can be calculated by multiplying its cross-sectional area by its total length. We can find the volume of the prism using the following steps: