Total Surface Area of Pentagonal Prism Calculator

✖The Base Edge Length of Pentagonal Prism is the length of the straight line connecting any two adjacent vertices of the base of the Pentagonal Prism.ⓘ Base Edge Length of Pentagonal Prism [l_e(Base)]			+10% -10%
✖The Height of Pentagonal Prism is the length of the straight line connecting any base vertex to the corresponding top vertex of the Pentagonal Prism.ⓘ Height of Pentagonal Prism [h]			+10% -10%

✖The Total Surface Area of Pentagonal Prism is the total amount of two-dimensional space occupied by all the faces of the Pentagonal Prism.ⓘ Total Surface Area of Pentagonal Prism [TSA]

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Formula

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Total Surface Area of Pentagonal Prism

Formula

`"TSA" = (5*"l"_{"e(Base)"}*"h")+sqrt(5*(5+(2*sqrt(5))))/2*"l"_{"e(Base)"}^2`

Example

`"1094.095m²"=(5*"10m"*"15m")+sqrt(5*(5+(2*sqrt(5))))/2*("10m")^2`

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Total Surface Area of Pentagonal Prism Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Pentagonal Prism = (5*Base Edge Length of Pentagonal Prism*Height of Pentagonal Prism)+sqrt(5*(5+(2*sqrt(5))))/2*Base Edge Length of Pentagonal Prism^2
TSA = (5*l_e(Base)*h)+sqrt(5*(5+(2*sqrt(5))))/2*l_e(Base)^2
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Total Surface Area of Pentagonal Prism - (Measured in Square Meter) - The Total Surface Area of Pentagonal Prism is the total amount of two-dimensional space occupied by all the faces of the Pentagonal Prism.
Base Edge Length of Pentagonal Prism - (Measured in Meter) - The Base Edge Length of Pentagonal Prism is the length of the straight line connecting any two adjacent vertices of the base of the Pentagonal Prism.
Height of Pentagonal Prism - (Measured in Meter) - The Height of Pentagonal Prism is the length of the straight line connecting any base vertex to the corresponding top vertex of the Pentagonal Prism.

STEP 1: Convert Input(s) to Base Unit

Base Edge Length of Pentagonal Prism: 10 Meter --> 10 Meter No Conversion Required
Height of Pentagonal Prism: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (5*l_e(Base)*h)+sqrt(5*(5+(2*sqrt(5))))/2*l_e(Base)^2 --> (5*10*15)+sqrt(5*(5+(2*sqrt(5))))/2*10^2

Evaluating ... ...

TSA = 1094.09548011779

STEP 3: Convert Result to Output's Unit

1094.09548011779 Square Meter --> No Conversion Required

FINAL ANSWER

1094.09548011779 ≈ 1094.095 Square Meter <-- Total Surface Area of Pentagonal Prism

(Calculation completed in 00.020 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Vellore Institute of Technology (VIT), Bhopal

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< 4 Pentagonal Prism Calculators

Total Surface Area of Pentagonal Prism

Go Total Surface Area of Pentagonal Prism = (5*Base Edge Length of Pentagonal Prism*Height of Pentagonal Prism)+sqrt(5*(5+(2*sqrt(5))))/2*Base Edge Length of Pentagonal Prism^2

Volume of Pentagonal Prism

Go Volume of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2*Height of Pentagonal Prism

Base Area of Pentagonal Prism

Go Base Area of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2

Lateral Surface Area of Pentagonal Prism

Go Lateral Surface Area of Pentagonal Prism = 5*Base Edge Length of Pentagonal Prism*Height of Pentagonal Prism

Total Surface Area of Pentagonal Prism Formula

What is Pentagonal Prism?

In geometry, the Pentagonal Prism is a prism with pentagonal base. This polyhedron has 7 faces, 15 edges, and 10 vertices.

What is Prism?

In mathematics, a Prism is a polyhedron with two polygonal bases parallel to each other. In physics (optics), a prism is defined as the transparent optical element with flat polished surfaces that refract light. Lateral faces join the two polygonal bases. The lateral faces are mostly rectangular. In some cases, it may be a parallelogram.

How to Calculate Total Surface Area of Pentagonal Prism?

Total Surface Area of Pentagonal Prism calculator uses Total Surface Area of Pentagonal Prism = (5*Base Edge Length of Pentagonal Prism*Height of Pentagonal Prism)+sqrt(5*(5+(2*sqrt(5))))/2*Base Edge Length of Pentagonal Prism^2 to calculate the Total Surface Area of Pentagonal Prism, The Total Surface Area of Pentagonal Prism formula is defined as the total amount of two-dimensional space occupied by all the faces of the Pentagonal Prism. Total Surface Area of Pentagonal Prism is denoted by TSA symbol.

How to calculate Total Surface Area of Pentagonal Prism using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Prism, enter Base Edge Length of Pentagonal Prism (l_e(Base)) & Height of Pentagonal Prism (h) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Prism calculation can be explained with given input values -> 1094.095 = (5*10*15)+sqrt(5*(5+(2*sqrt(5))))/2*10^2.

FAQ

What is Total Surface Area of Pentagonal Prism?

The Total Surface Area of Pentagonal Prism formula is defined as the total amount of two-dimensional space occupied by all the faces of the Pentagonal Prism and is represented as TSA = (5*l_e(Base)*h)+sqrt(5*(5+(2*sqrt(5))))/2*l_e(Base)^2 or Total Surface Area of Pentagonal Prism = (5*Base Edge Length of Pentagonal Prism*Height of Pentagonal Prism)+sqrt(5*(5+(2*sqrt(5))))/2*Base Edge Length of Pentagonal Prism^2. The Base Edge Length of Pentagonal Prism is the length of the straight line connecting any two adjacent vertices of the base of the Pentagonal Prism & The Height of Pentagonal Prism is the length of the straight line connecting any base vertex to the corresponding top vertex of the Pentagonal Prism.

How to calculate Total Surface Area of Pentagonal Prism?

The Total Surface Area of Pentagonal Prism formula is defined as the total amount of two-dimensional space occupied by all the faces of the Pentagonal Prism is calculated using Total Surface Area of Pentagonal Prism = (5*Base Edge Length of Pentagonal Prism*Height of Pentagonal Prism)+sqrt(5*(5+(2*sqrt(5))))/2*Base Edge Length of Pentagonal Prism^2. To calculate Total Surface Area of Pentagonal Prism, you need Base Edge Length of Pentagonal Prism (l_e(Base)) & Height of Pentagonal Prism (h). With our tool, you need to enter the respective value for Base Edge Length of Pentagonal Prism & Height of Pentagonal Prism and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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