We all love Toblerone. You can't say no to Toblerone, right? However, we want you to focus on the Toblerone wrappers. That is a very unique shape and this unique shape makes this chocolate special. The question is, what is that shape? We call it Prism. Now you might be wondering what is a prism? Let's talk about it.

What is a Prism?

Prisms are polyhedra that have two parallel, equally sized faces called bases and their lateral faces are parallelograms. Let's simplify it, the top and the bottom part of the prism is called the base. The base of the prism can be any polygon. It can be any type of polygon, it can be a hexagon, or maybe a pentagon, etc. but one thing is for sure, it will be a polygon. All the faces, except the base faces, are called lateral faces and they will always be parallelograms. These parallelograms will be equal in all dimensions. The height of a prism is the distance between the bases and the lateral edges of a prism are equally sized parallel edges. Below is a picture of a prism.

The best Maths tutors available
Intasar
4.9
4.9 (33 reviews)
Intasar
£45
/h
Gift icon
1st lesson free!
Paolo
4.9
4.9 (18 reviews)
Paolo
£30
/h
Gift icon
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£27
/h
Gift icon
1st lesson free!
Jamie
5
5 (16 reviews)
Jamie
£25
/h
Gift icon
1st lesson free!
Dr. Kritaphat
4.9
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
Gift icon
1st lesson free!
Shane
5
5 (15 reviews)
Shane
£15
/h
Gift icon
1st lesson free!
Farooq
4.9
4.9 (17 reviews)
Farooq
£40
/h
Gift icon
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£30
/h
Gift icon
1st lesson free!
Intasar
4.9
4.9 (33 reviews)
Intasar
£45
/h
Gift icon
1st lesson free!
Paolo
4.9
4.9 (18 reviews)
Paolo
£30
/h
Gift icon
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£27
/h
Gift icon
1st lesson free!
Jamie
5
5 (16 reviews)
Jamie
£25
/h
Gift icon
1st lesson free!
Dr. Kritaphat
4.9
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
Gift icon
1st lesson free!
Shane
5
5 (15 reviews)
Shane
£15
/h
Gift icon
1st lesson free!
Farooq
4.9
4.9 (17 reviews)
Farooq
£40
/h
Gift icon
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£30
/h
Gift icon
1st lesson free!
Let's go

Unfold of a Prism

Unfolding a 3-dimensional shape is fun. You always get something which is interesting as well as satisfying to look at, well most of the time. The more complex the geometry, the more beautiful the unfolding. Without any further ado, let's open this figure and unreal its secrets.

The above figure represents an unfolded prism. The above figure looks like a division sign, right?

Types of Prisms

Prism is a very generic shape and that is why it contains many variations. These variations in the shape make it special. Let's take a look at some common types of prisms.

Regular Prisms

The bases of the regular prisms are regular polygons.

Irregular Prisms

The bases of the irregular prisms are irregular polygons.

Right Prisms

The lateral faces of the right prisms are rectangles or squares.

Oblique Prisms

The lateral faces of the oblique prisms are rhomboids or rhombi.

Parallelepipeds

The bases of parallelepiped prisms are parallelograms.

Cuboid

The faces of cuboids are rectangular faces.

Types of Prisms by Their Base

As mentioned before, prisms consist of two different shapes, one is the base and the other is the faces. The base of the prims can be transformed into many polygons and that is why, under this heading, we will teach you about types of prisms by their base.

Triangular Prism

The bases are triangles.

Square Prism

The bases are squares.

Pentagonal Prism

The bases are pentagons.

Hexagonal Prism

The bases are hexagons.

Lateral Area of a Prism

The lateral area is the area of a prism without its top and bottom bases. In simple words, the lateral area of a prism is the area of all faces except the bases. To find the lateral area, you will need the perimeter of the base and the height of the prism. The lateral area is the product of the perimeter of the base and height of the prism.

{ A }_{ L } = { P }_{ B } \times h

Surface Area of a Prism

Surface area means the space occupied by the shape's boundary only. To find the surface area of the prism, you need to add all the faces as well as both bases of a prism.

{ A }_{ T } = { A }_{ L } + 2 \times { A }_{ B } or { A }_{ T } = { A }_{ L } = { P }_{ B } \times h + 2 \times { A }_{ B }

Volume of a Prism

The volume of an object means the total space occupied by an object. Finding volume is simple, all you need to do is to multiply the base area with the height.

V = { A }_{ B } \times h

Examples

Calculate the height of a prism whose base has an area of 12 dm² and whose capacity is 48 liters.

48 l  = 48 { dm }^{ 3 }

48 = 12 \times h \qquad h = \frac { 48 }{ 12 } = 4 dm

 

Calculate the lateral area, surface area and volume of a prism whose base is a rhombus with diagonals of 12 and 18 cm.

 

{ l }^{ 2 } = { 9 }^{ 2 } + { 6 }^{ 2 }

l = \sqrt { { 9 }^{ 2 } + { 6 }^{ 2 } } = 10.82 cm

{ A }_{ L } = { P }_{ B } \times h

{ P }_{ B } = 24 + 10.82 = 34.82 cm

{ A }_{ L } = 34.82 \times 4 = 1,038.72 { cm }^{ 2 }

{ A }_{ T } = { A }_{ L } + 2 \times { A }_{ B }

{ A }_{ B } = \frac { 18 \times 12 }{ 2 } = 108 { cm }^{ 2 }

{ A }_{ T } = 1,038.72 + 2 \times 108 = 1,254.72 { cm }^{ 2 }

V = { A }_{ B } \times h

V = 108 \times 24 = 2592 { cm }^{ 3 }

>

The platform that connects tutors and students

Did you like this article? Rate it!

1 Star2 Stars3 Stars4 Stars5 Stars 4.00 (3 rating(s))
Loading...

Hamza

Hi! I am Hamza and I am from Pakistan. My hobbies are reading, writing and playing chess. Currently, I am a student enrolled in the Chemical Engineering Bachelor program.