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Total Surface Area of Star Pyramid Formula

GoTotal Surface Area of Star Pyramid given Chord Length Formula

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Total Surface Area of Star Pyramid is the total amount of two-dimensional space occupied on all the faces of the Star Pyramid. Check FAQs

TSA = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(l e(Base) \cdot [phi])}^{2}}{2}) + (10 \cdot \sqrt{(\frac{l e(Base) + l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Lateral) + l e(Ridge) - l e(Base)}{2}) \cdot (\frac{l e(Base) - l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Base) + l e(Lateral) - l e(Ridge)}{2})})

TSA - Total Surface Area of Star Pyramid?l_e(Base) - Edge Length of Base of Star Pyramid?l_e(Lateral) - Lateral Edge Length of Star Pyramid?l_e(Ridge) - Ridge Length of Star Pyramid?[phi] - Golden ratio?

Total Surface Area of Star Pyramid Example

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Here is how the Total Surface Area of Star Pyramid equation looks like with Values.

Here is how the Total Surface Area of Star Pyramid equation looks like with Units.

Here is how the Total Surface Area of Star Pyramid equation looks like.

310.746 = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(6 \cdot 1.618)}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})

310.746m² = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(6m \cdot 1.618)}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6m + 11m + 8m}{2}) \cdot (\frac{11m + 8m - 6m}{2}) \cdot (\frac{6m - 11m + 8m}{2}) \cdot (\frac{6m + 11m - 8m}{2})})

310.746 = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(6 \cdot 1.618)}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})

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Total Surface Area of Star Pyramid Solution

Follow our step by step solution on how to calculate Total Surface Area of Star Pyramid?

FIRST Step Consider the formula

TSA = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(l e(Base) \cdot [phi])}^{2}}{2}) + (10 \cdot \sqrt{(\frac{l e(Base) + l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Lateral) + l e(Ridge) - l e(Base)}{2}) \cdot (\frac{l e(Base) - l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Base) + l e(Lateral) - l e(Ridge)}{2})})

Next Step Substitute values of Variables

∴

TSA = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(6m \cdot [phi])}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6m + 11m + 8m}{2}) \cdot (\frac{11m + 8m - 6m}{2}) \cdot (\frac{6m - 11m + 8m}{2}) \cdot (\frac{6m + 11m - 8m}{2})})

Next Step Substitute values of Constants

∴

TSA = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(6m \cdot 1.618)}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6m + 11m + 8m}{2}) \cdot (\frac{11m + 8m - 6m}{2}) \cdot (\frac{6m - 11m + 8m}{2}) \cdot (\frac{6m + 11m - 8m}{2})})

Next Step Prepare to Evaluate

∴

TSA = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(6 \cdot 1.618)}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})

Next Step Evaluate

∴

TSA = 310.745997691624m²

LAST Step Rounding Answer

∴

TSA = 310.746m²

Total Surface Area of Star Pyramid Formula Elements

Variables

Constants

Functions

Total Surface Area of Star Pyramid

Total Surface Area of Star Pyramid is the total amount of two-dimensional space occupied on all the faces of the Star Pyramid.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Star Pyramid

Edge Length of Base of Star Pyramid

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.

Symbol: l_e(Base)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Base of Star Pyramid

Lateral Edge Length of 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.

Symbol: l_e(Lateral)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Lateral Edge Length of Star Pyramid

Ridge Length of 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.

Symbol: l_e(Ridge)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Ridge Length of Star Pyramid

Golden ratio

The Golden ratio occurs when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

Symbol: [phi]

Value: 1.61803398874989484820458683436563811

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.

Syntax: sqrt(Number)

Other Formulas to find Total Surface Area of Star Pyramid

Go Total Surface Area of Star Pyramid given Chord Length

TSA = (\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{l c}^{2}}{2}) + (10 \cdot \sqrt{(\frac{l e(Base) + l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Lateral) + l e(Ridge) - l e(Base)}{2}) \cdot (\frac{l e(Base) - l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Base) + l e(Lateral) - l e(Ridge)}{2})})

How to Evaluate Total Surface Area of Star Pyramid?

Total Surface Area of Star Pyramid evaluator 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 evaluate 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 evaluate Total Surface Area of Star Pyramid using this online evaluator? To use this online evaluator 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.

FAQs on Total Surface Area of Star Pyramid

What is the formula to find Total Surface Area of Star Pyramid?

The formula of Total Surface Area of Star Pyramid is expressed as 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))). Here is an example- 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))).

How to calculate Total Surface Area of Star Pyramid?

With 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)) we can find Total Surface Area of Star Pyramid using the formula - 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))). This formula also uses Golden ratio constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Star Pyramid?

Here are the different ways to Calculate Total Surface Area of Star Pyramid-

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)))

Can the Total Surface Area of Star Pyramid be negative?

No, the Total Surface Area of Star Pyramid, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Star Pyramid?

Total Surface Area of Star Pyramid is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Star Pyramid can be measured.

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Total Surface Area of Star Pyramid Formula

​GoTotal Surface Area of Star Pyramid given Chord Length Formula

Total Surface Area of Star Pyramid Example

Total Surface Area of Star Pyramid Solution

Total Surface Area of Star Pyramid Formula Elements

Other Formulas to find Total Surface Area of Star Pyramid

How to Evaluate Total Surface Area of Star Pyramid?

FAQs on Total Surface Area of Star Pyramid

Variable Name

GoTotal Surface Area of Star Pyramid given Chord Length Formula