Total Surface Area of Star Pyramid Calculator

✖Edge Length of Base of Star Pyramid is the length of the line joining any two adjacent vertices of the pentagrammic base of the Star Pyramid.ⓘ Edge Length of Base of Star Pyramid [l_e(Base)]			+10% -10%
✖Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid.ⓘ Lateral Edge Length of Star Pyramid [l_e(Lateral)]			+10% -10%
✖Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid.ⓘ Ridge Length of Star Pyramid [l_e(Ridge)]			+10% -10%

✖Total Surface Area of Star Pyramid is the total amount of two-dimensional space occupied on all the faces of the Star Pyramid.ⓘ Total Surface Area of Star Pyramid [TSA]

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Total Surface Area of Star Pyramid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Edge Length of Base of Star Pyramid*[phi])^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2)))
TSA = ((sqrt(5*(5-(2*sqrt(5))))*(l_e(Base)*[phi])^2)/2)+(10*sqrt(((l_e(Base)+l_e(Lateral)+l_e(Ridge))/2)*((l_e(Lateral)+l_e(Ridge)-l_e(Base))/2)*((l_e(Base)-l_e(Lateral)+l_e(Ridge))/2)*((l_e(Base)+l_e(Lateral)-l_e(Ridge))/2)))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811

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 Star Pyramid - (Measured in Square Meter) - Total Surface Area of Star Pyramid is the total amount of two-dimensional space occupied on all the faces of the Star Pyramid.
Edge Length of Base of Star Pyramid - (Measured in Meter) - Edge Length of Base of Star Pyramid is the length of the line joining any two adjacent vertices of the pentagrammic base of the Star Pyramid.
Lateral Edge Length of Star Pyramid - (Measured in Meter) - Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid.
Ridge Length of Star Pyramid - (Measured in Meter) - Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Base of Star Pyramid: 6 Meter --> 6 Meter No Conversion Required
Lateral Edge Length of Star Pyramid: 11 Meter --> 11 Meter No Conversion Required
Ridge Length of Star Pyramid: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = ((sqrt(5*(5-(2*sqrt(5))))*(l_e(Base)*[phi])^2)/2)+(10*sqrt(((l_e(Base)+l_e(Lateral)+l_e(Ridge))/2)*((l_e(Lateral)+l_e(Ridge)-l_e(Base))/2)*((l_e(Base)-l_e(Lateral)+l_e(Ridge))/2)*((l_e(Base)+l_e(Lateral)-l_e(Ridge))/2))) --> ((sqrt(5*(5-(2*sqrt(5))))*(6*[phi])^2)/2)+(10*sqrt(((6+11+8)/2)*((11+8-6)/2)*((6-11+8)/2)*((6+11-8)/2)))

Evaluating ... ...

TSA = 310.745997691624

STEP 3: Convert Result to Output's Unit

310.745997691624 Square Meter --> No Conversion Required

FINAL ANSWER

310.745997691624 ≈ 310.746 Square Meter <-- Total Surface Area of Star Pyramid

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Surface Area of Star Pyramid Calculators

Total Surface Area of Star Pyramid

LaTeX Go Total Surface Area of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Edge Length of Base of Star Pyramid*[phi])^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2)))

Total Surface Area of Star Pyramid given Chord Length

LaTeX Go Total Surface Area of Star Pyramid = (sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2)))

Total Surface Area of Star Pyramid Formula

LaTeX Go

What is a Star Pyramid?

A Star Pyramid is based on a regular pentagram and is concave. It is a pyramid with a pentagrammic base. It has 11 faces which include a pentagram base surface and 10 triangular surfaces. Also, It has 20 edges and 6 vertices.

How to Calculate Total Surface Area of Star Pyramid?

Total Surface Area of Star Pyramid calculator uses Total Surface Area of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Edge Length of Base of Star Pyramid*[phi])^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))) to calculate the Total Surface Area of Star Pyramid, Total Surface Area of Star Pyramid formula is defined as the total amount of two-dimensional space occupied on all the faces of the Star Pyramid. Total Surface Area of Star Pyramid is denoted by TSA symbol.

How to calculate Total Surface Area of Star Pyramid using this online calculator? To use this online calculator for Total Surface Area of Star Pyramid, enter Edge Length of Base of Star Pyramid (l_e(Base)), Lateral Edge Length of Star Pyramid (l_e(Lateral)) & Ridge Length of Star Pyramid (l_e(Ridge)) and hit the calculate button. Here is how the Total Surface Area of Star Pyramid calculation can be explained with given input values -> 310.746 = ((sqrt(5*(5-(2*sqrt(5))))*(6*[phi])^2)/2)+(10*sqrt(((6+11+8)/2)*((11+8-6)/2)*((6-11+8)/2)*((6+11-8)/2))).

FAQ

What is Total Surface Area of Star Pyramid?

Total Surface Area of Star Pyramid formula is defined as the total amount of two-dimensional space occupied on all the faces of the Star Pyramid and is represented as TSA = ((sqrt(5*(5-(2*sqrt(5))))*(l_e(Base)*[phi])^2)/2)+(10*sqrt(((l_e(Base)+l_e(Lateral)+l_e(Ridge))/2)*((l_e(Lateral)+l_e(Ridge)-l_e(Base))/2)*((l_e(Base)-l_e(Lateral)+l_e(Ridge))/2)*((l_e(Base)+l_e(Lateral)-l_e(Ridge))/2))) or Total Surface Area of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Edge Length of Base of Star Pyramid*[phi])^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))). Edge Length of Base of Star Pyramid is the length of the line joining any two adjacent vertices of the pentagrammic base of the Star Pyramid, Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid & Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid.

How to calculate Total Surface Area of Star Pyramid?

Total Surface Area of Star Pyramid formula is defined as the total amount of two-dimensional space occupied on all the faces of the Star Pyramid is calculated using Total Surface Area of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Edge Length of Base of Star Pyramid*[phi])^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))). To calculate Total Surface Area of Star Pyramid, you need Edge Length of Base of Star Pyramid (l_e(Base)), Lateral Edge Length of Star Pyramid (l_e(Lateral)) & Ridge Length of Star Pyramid (l_e(Ridge)). With our tool, you need to enter the respective value for Edge Length of Base of Star Pyramid, Lateral Edge Length of Star Pyramid & Ridge Length of Star Pyramid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Total Surface Area of Star Pyramid?

In this formula, Total Surface Area of Star Pyramid uses Edge Length of Base of Star Pyramid, Lateral Edge Length of Star Pyramid & Ridge Length of Star Pyramid. We can use 1 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Star Pyramid = (sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2)))

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