Since a is positive, the value of a = -16√3 is admissible. Therefore, either, a = - 16√3 or, a = 8√3 = (6a²/4) cot (π/4), Īccording to problem, the area of the whole surface of the prism = 1152√3 Here, the area of its base = area of the regular hexagon and the area of side-faces of the prism

Solution: Let us take 'a' be the length of a side of the regular hexagon. The area of the whole surface of the prism is 1152√3 sq.cm. It stands on a base which is a regular hexagon. The volume of square prism = Base area × heightĮxample 3: A right prism has a height of 12 cm. Now by calculating the height of the square prism, we get, Therefore, the volume of a triangular prism = 400 cm 3.Įxample 2: The volume of a square is 400 cm 3 and the base area is 80 cm 2? Can you calculate its height? (V) volume of a prism = Base area × Height cubic units We will concentrate on some of the examples of prism to get some good understanding about it.Įxample 1: The area of a triangular prism is 50 cm 2 and height is 8 cm? Can you find the volume? The volume of a Hexagonal Prism = 3abh cubic unitsĪ = Apothem length of the hexagonal prism. There are six rectangular faces and two parallel hexagonal bases in a hexagonal prism. H = Height of the pentagonal prism Volume of a Hexagonal Prism So, the Volume of a Pentagonal Prism = (5/2) abh cubic unitsĪ = Apothem length of the pentagonal prism. There are five rectangular faces and two parallel pentagonal bases in a Pentagonal Prism. H = height of a triangular prism Volume of a Pentagonal Prism The volume of a Triangular Prism = (½) abh cubic units. The formula for the volume of a triangular prism is given as: H = height of a rectangular prism Volume of a Triangular PrismĪ triangular prism has got three rectangular faces and two triangular bases. So, the volume of a Rectangular Prism = lbh cubic units. The rectangular prism is also called “Cuboid”. There are four rectangular faces and two parallel rectangular bases in a rectangular prism. Here, we will concentrate on the rectangular prism, triangular prism, pentagonal prism, and so on. Now, we will discuss the formula of the volume of a prism.

Therefore, the volume of a Prism = Base Area × Length Volume of a Prism Formula So, in math, it is the product of the area of the base and the length. The total space which is occupied by the three-dimensional object is called the volume of a prism. So, the formula of the Surface Area of a Prism = 2(Base Area) + (Base perimeter × length) The total area which is covered by the faces of the prism is the surface area of the prism.

It is because of the three-dimensional shape, the prism has both the properties, which are volume and surface area. It is based on the surface area and volume of the prism for which the formulas are defined. The side faces are parallelograms.īased on the shape of the bases, prisms are further classified as below:

Oblique Prism: In this type of prism, the faces and the joining edges are not perpendicular to the base faces.

Right Prism: Right prism is the one whose faces and the joining edges are perpendicular to the base faces.

The classification of the prism can be further done into two types which are Right Prism and Oblique Prism

Irregular Prism: An irregular prism has the base in the shape of an irregular polygon.

Regular Prism: A regular prism is the one where the bases of the prism are in the shape of a regular polygon.

We will have a look at these types of prisms as below: Therefore, it should be kept in mind that a prism can be rectangular, cubic, pentagonal as well as other polygon shapes, excluding the circular shape.īased on the cross-sections, the prisms are of two types which are Regular Prism and Irregular Prism. The shape of the prism does not have any curve. It is also called triangular prism as the cross-section looks like a triangle. What is the shape of the prism?Ī prism has got a solid shape where it consists of two equal ends as well as identical cross-section and flat faces or surfaces. In case you wish to take the cross-section or the prism parallel to the base, then you would find that the cross-sections would look like the bases. Without the bases, the faces are parallelograms. It is the combination of the identical bases, flat faces and same cross-sections. The three-dimensional solid object whose two ends are exactly of the same shape is the prism. We would also work on the examples of the prism where it would make things quite clear to you. Students would also be able to learn about the volume of the prism.

Calculate volume of a prism