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Prism Surface Area Calculator

Introduction

Welcome to our Prism Surface Area Calculator, which will help you calculate the surface area for different types of Prisms. A prism is a solid three-dimensional shape with polygons as bases on either end of the prism. The bases are congruent and parallel to each other. The bases are connected by the prism’s lateral faces.

There are different types of prisms, classified based on the shape of their bases.

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

How to use this Calculator?

Using the Prism Surface Area calculator, you can calculate the prism’s lateral surface area and total surface area by inputting the values of the required variables for the specific type of Prism.

Triangular Prism Surface Area Calculator

You can calculate the lateral surface area and the total surface area of the triangular prism by inputting the required value for the calculation.

The variables in the calculator include

First Edge Length (S1) Length of the 1st side of the Triangular Base.

Second Edge Length (S2) Length of the 2nd side of the Triangular Base.

Third Edge Length (S3) Length of the 3rd side of the Triangular Base.

Length (l) The length of the Prism.

Base (b) The length of the bottom edge of the triangular base.

Height (h) The height of the triangular base.

Lateral Surface Area (LSA) The lateral surface area is the area of the lateral faces of the Prism.

Total Surface Area (TSA) The total surface area of the Prism is the sum of the lateral surface area and the area of the two bases.

Square Prism Surface Area Calculator

You can calculate the lateral surface area and the total surface area of the Square prism by inputting the required value for the calculation.

The variables in the calculator include

Side (a) The length of one of the sides of the Square Base.

Height (h) The height of the prism.

Lateral Surface Area (LSA) The lateral surface area is the area of the lateral faces of the Prism.

Total Surface Area (TSA) The total surface area of the Prism is the sum of the lateral surface area and the area of the two bases.

Rectangular Prism Surface Area Calculator

You can calculate the lateral surface area and the total surface area of the Rectangular prism by inputting the required value for the calculation.

The variables in the calculator include

Length (l) The length of the Rectangular Base.

Breadth (b) The breadth of the Rectangular Base.

Height (h) The height of the prism.

Lateral Surface Area (LSA) The lateral surface area is the area of the lateral faces of the Prism.

Total Surface Area (TSA) The total surface area of the Prism is the sum of the lateral surface area and the area of the two bases.

Pentagonal Prism Surface Area Calculator

You can calculate the lateral surface area and the total surface area of the Pentagonal prism by inputting the required value for the calculation.

The variables in the calculator include

Base Length (a) The length of the side of the Pentagonal base.

Height (h) The height of the prism.

Lateral Surface Area (LSA) The lateral surface area is the area of the lateral faces of the Prism.

Total Surface Area (TSA) The total surface area of the Prism is the sum of the lateral surface area and the area of the two bases.

Hexagonal Prism Surface Area Calculator

You can calculate the lateral surface area and the total surface area of the hexagonal prism by inputting the required value for the calculation.

The variables in the calculator include

Base Length (a) The length of the side of the Hexagonal base.

Height (h) The height of the prism.

Lateral Surface Area (LSA) The lateral surface area is the area of the lateral faces of the Prism.

Total Surface Area (TSA) The total surface area of the Prism is the sum of the lateral surface area and the area of the two bases.

Octagonal Prism Surface Area Calculator

You can calculate the lateral surface area and the total surface area of the Octagonal prism by inputting the required value for the calculation.

The variables in the calculator include

Base Length (a) The length of the side of the Octagonal base.

Height (h) The height of the prism.

Lateral Surface Area (LSA) The lateral surface area is the area of the lateral faces of the Prism.

Total Surface Area (TSA) The total surface area of the Prism is the sum of the lateral surface area and the area of the two bases.

What is a Prism?

A Prism is a solid three-dimensional shape with identical polygons as bases at both ends of the Prism. The bases are congruent and parallel to each other, and they are connected by the lateral faces of the prism.

Types of Prisms

Type of Polygon of the Base

Prisms can be classified based on the type of polygon of the base.

  1. Regular Prism: If the prism’s base is in the shape of a regular polygon, where all sides are equal, then it is called a regular prism.
  2. Irregular Prism: If the prism’s base has the shape of an irregular polygon, where all sides are not equal, then the prism is called an irregular prism.

The shape of the Base

Prisms can also be classified based on the shape of the base.

  1. Triangular Prism: A prism that has a base that is triangular in shape is called a triangular prism.
  2. Square Prism: A prism that has a base that is square in shape is called a square prism.
  3. Rectangular Prism: A prism that has a base that is rectangular in shape is called a rectangular prism.
  4. Pentagonal Prism: A prism that has a base that is pentagonal in shape is called a pentagonal prism.
  5. Hexagonal Prism: A prism that has a base that is hexagonal in shape is called a hexagonal prism.
  6. Octagonal Prism: A prism that has a base that is octagonal in shape is called an octagonal prism.

Alignment of the base

Prisms are also classified based on the alignment of the lateral faces with the base.

  1. Right Prism: if the joining edges of the base are perpendicular to it, then it is called a right prism. The lateral faces are perpendicular to the base.
  2. Oblique Prism: if the lateral faces are aligned at an angle with the base, it is known as an oblique prism.

How are the Lateral Surface Area and Total Surface Area of the Prism Calculated?

Lateral Surface Area (LSA)

The lateral surface area is the area of the prism without including the area of the bases. The lateral surface area for a prism is based of the following formula

LSA=Perimeter of the Base * Length of the Prism\text{LSA} = \text{Perimeter of the Base * Length of the Prism}

Total Surface Area (TSA)

The total surface area of the Prism is the sum of the lateral surface area and the area of the two bases. The total surface area for a prism is based of the following formula

TSA=(Perimeter of base * Length of prism) + (2 * Base Area)\text{TSA} = \text{(Perimeter of base * Length of prism) + (2 * Base Area)}

Triangular Prism Lateral and Total Surface Area

We calculate the lateral surface area of the triangular prism using the following formula

LSA=(S1+S2+S3)∗l\text{LSA} = (S_1 + S_2 + S_3)*l

Where,

S1 = Length of 1st side of Triangular Base

S2 = Length of 2nd side of Triangular Base

S3 = Length of 3rd side of Triangular Base

l = height/length of the Prism

We calculate the total surface area of the triangular prism using the following formula.

TSA=(S1+S2+S3)∗l+bh\text{TSA} = (S_1 + S_2 + S_3)*l + bh

Where,

S1 = Length of 1st side of Triangular Base

S2 = Length of 2nd side of Triangular Base

S3 = Length of 3rd side of Triangular Base

l = height/length of the Prism

b = Length of Triangular Base, it could be any of the Sides S1, S2, or S3.

h = height of a triangle with respect to chosen side b.

Square Prism Lateral and Total Surface Area

We calculate the lateral surface area of the square prism using the following formula

LSA=4ah\text{LSA} = 4ah

Where,

a = Length of the Side of Square

h = height of the Prism

We calculate the total surface area of the square prism using the following formula.

TSA=4ah+2a2\text{TSA} = 4ah + 2a^2

Where,

a = Length of the Side of Square

h = height of the Prism

Rectangular Prism Lateral and Total Surface Area

We calculate the lateral surface area of the rectangular prism using the following formula

LSA=2(l+b)h\text{LSA} = 2(l + b)h

Where,

l = Length of the rectangular base

b = breadth of the rectangular base

h = height of the prism

We calculate the total surface area of the rectangular prism using the following formula.

TSA=2(lb+bh+lh)\text{TSA} = 2(lb + bh + lh)

Where,

l = Length of the rectangular base

b = breadth of the rectangular base

h = height of the prism

Pentagonal Prism Lateral and Total Surface Area

We calculate the lateral surface area of the pentagonal prism using the following formula

LSA=5bh\text{LSA} = 5bh

Where,

b = Length of the side of the Pentagon

h = height of the prism

We calculate the total surface area of the pentagonal prism using the following formula.

TSA=5bh+125+(5+25)  b2\text{TSA} = 5bh + \normalsize \dfrac{1}{2} \sqrt{5 + (5+2\sqrt{5})}\; b^2

Where,

b = Length of the side of the Pentagon

h = height of the prism

Hexagonal Prism Lateral and Total Surface Area

We calculate the lateral surface area of the hexagonal prism using the following formula

LSA=6bh\text{LSA} = 6bh

Where,

b = Length of the side of the hexagon

h = height of the prism

We calculate the total surface area of the hexagonal prism using the following formula.

TSA=6bh+33  b2\text{TSA} = 6bh + 3 \sqrt{3}\;b^2

Where,

b = Length of the side of the hexagon

h = height of the prism

Octagonal Prism Lateral and Total Surface Area

We calculate the lateral surface area of the octagonal prism using the following formula

LSA=8bh\text{LSA} = 8bh

Where,

b = Length of the side of the octagon

h = height of the prism

We calculate the total surface area of the octagonal prism using the following formula.

TSA=8bh+4(1+2)  b2\text{TSA} = 8bh + 4(1+\sqrt{2})\;b^2

Where,

b = Length of the side of the octagon

h = height of the prism

Examples

Given a rectangular prism with a base length of 6 cm, a width of 5 cm, and a prism length of 7 cm. What is the lateral and total surface area of the prism?

We calculate the lateral surface area of the rectangular prism using the following formula

LSA=2(l+b)h=2∗(6+5)∗7=154  cm2 \begin{aligned} \text{LSA} &= 2(l + b)h \\[10pt] &= 2 * (6 + 5) * 7 \\[10pt] &= 154 \; cm^2 \end{aligned}

We calculate the total surface area of the rectangular prism using the following formula.

TSA=2(lb+bh+lh)=2(6⋅5+5⋅7+6⋅7)=214  cm2\begin{aligned} \text{TSA} &= 2(lb + bh + lh) \\[10pt] &= 2(6\cdot 5 + 5\cdot 7 + 6 \cdot 7) \\[10pt] &= 214 \; cm^2 \end{aligned}
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