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Slant Height of Square Pyramid given Total Surface Area Formula

GoSlant Height of Square Pyramid Formula

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Slant Height of Square Pyramid is the length measured along the lateral face from the base to the apex of the Square Pyramid along the center of the face. Check FAQs

h slant = \sqrt{\frac{{l e(Base)}^{2}}{4} + \frac{{(\frac{TSA - {l e(Base)}^{2}}{l e(Base)})}^{2} - {l e(Base)}^{2}}{4}}

h_slant - Slant Height of Square Pyramid?l_e(Base) - Edge Length of Base of Square Pyramid?TSA - Total Surface Area of Square Pyramid?

Slant Height of Square Pyramid given Total Surface Area Example

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Here is how the Slant Height of Square Pyramid given Total Surface Area equation looks like with Values.

Here is how the Slant Height of Square Pyramid given Total Surface Area equation looks like with Units.

Here is how the Slant Height of Square Pyramid given Total Surface Area equation looks like.

16 = \sqrt{\frac{10^{2}}{4} + \frac{{(\frac{420 - 10^{2}}{10})}^{2} - 10^{2}}{4}}

16m = \sqrt{\frac{{10m}^{2}}{4} + \frac{{(\frac{420m² - {10m}^{2}}{10m})}^{2} - {10m}^{2}}{4}}

16 = \sqrt{\frac{10^{2}}{4} + \frac{{(\frac{420 - 10^{2}}{10})}^{2} - 10^{2}}{4}}

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Slant Height of Square Pyramid given Total Surface Area Solution

Follow our step by step solution on how to calculate Slant Height of Square Pyramid given Total Surface Area?

FIRST Step Consider the formula

h slant = \sqrt{\frac{{l e(Base)}^{2}}{4} + \frac{{(\frac{TSA - {l e(Base)}^{2}}{l e(Base)})}^{2} - {l e(Base)}^{2}}{4}}

Next Step Substitute values of Variables

∴

h slant = \sqrt{\frac{{10m}^{2}}{4} + \frac{{(\frac{420m² - {10m}^{2}}{10m})}^{2} - {10m}^{2}}{4}}

Next Step Prepare to Evaluate

∴

h slant = \sqrt{\frac{10^{2}}{4} + \frac{{(\frac{420 - 10^{2}}{10})}^{2} - 10^{2}}{4}}

LAST Step Evaluate

∴

h slant = 16m

Slant Height of Square Pyramid given Total Surface Area Formula Elements

Variables

Functions

Slant Height of Square Pyramid

Slant Height of Square Pyramid is the length measured along the lateral face from the base to the apex of the Square Pyramid along the center of the face.

Symbol: h_slant

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Slant Height of Square Pyramid

Edge Length of Base of Square Pyramid

Edge Length of Base of Square Pyramid is the length of the straight line connecting any two adjacent vertices of the base of the Square Pyramid.

Symbol: l_e(Base)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Base of Square Pyramid

Total Surface Area of Square Pyramid

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Square Pyramid

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 Slant Height of Square Pyramid

Go Slant Height of Square Pyramid

h slant = \sqrt{\frac{{l e(Base)}^{2}}{4} + h^{2}}

Other formulas in Slant Height of Square Pyramid category

Go Lateral Edge Length of Square Pyramid

l e(Lateral) = \sqrt{\frac{{l e(Base)}^{2}}{2} + h^{2}}

Go Base Area of Square Pyramid

A Base = {l e(Base)}^{2}

Go Base Angle of Square Pyramid

∠ Base = \arccos (\frac{{(\frac{l e(Base)}{2})}^{2} + {h slant}^{2} - h^{2}}{l e(Base) \cdot h slant})

Go Edge Length of Base of Square Pyramid given Lateral Edge Length

l e(Base) = \sqrt{2 \cdot ({l e(Lateral)}^{2} - h^{2})}

How to Evaluate Slant Height of Square Pyramid given Total Surface Area?

Slant Height of Square Pyramid given Total Surface Area evaluator uses Slant Height of Square Pyramid = sqrt((Edge Length of Base of Square Pyramid^2)/4+(((Total Surface Area of Square Pyramid-Edge Length of Base of Square Pyramid^2)/Edge Length of Base of Square Pyramid)^2-Edge Length of Base of Square Pyramid^2)/4) to evaluate the Slant Height of Square Pyramid, Slant Height of Square Pyramid given Total Surface Area formula is defined as the length measured along the lateral face from the base to the apex of the Square Pyramid along the center of the face and is calculated using the total surface area of the Square Pyramid. Slant Height of Square Pyramid is denoted by h_slant symbol.

How to evaluate Slant Height of Square Pyramid given Total Surface Area using this online evaluator? To use this online evaluator for Slant Height of Square Pyramid given Total Surface Area, enter Edge Length of Base of Square Pyramid (l_e(Base)) & Total Surface Area of Square Pyramid (TSA) and hit the calculate button.

FAQs on Slant Height of Square Pyramid given Total Surface Area

What is the formula to find Slant Height of Square Pyramid given Total Surface Area?

The formula of Slant Height of Square Pyramid given Total Surface Area is expressed as Slant Height of Square Pyramid = sqrt((Edge Length of Base of Square Pyramid^2)/4+(((Total Surface Area of Square Pyramid-Edge Length of Base of Square Pyramid^2)/Edge Length of Base of Square Pyramid)^2-Edge Length of Base of Square Pyramid^2)/4). Here is an example- 16 = sqrt((10^2)/4+(((420-10^2)/10)^2-10^2)/4).

How to calculate Slant Height of Square Pyramid given Total Surface Area?

With Edge Length of Base of Square Pyramid (l_e(Base)) & Total Surface Area of Square Pyramid (TSA) we can find Slant Height of Square Pyramid given Total Surface Area using the formula - Slant Height of Square Pyramid = sqrt((Edge Length of Base of Square Pyramid^2)/4+(((Total Surface Area of Square Pyramid-Edge Length of Base of Square Pyramid^2)/Edge Length of Base of Square Pyramid)^2-Edge Length of Base of Square Pyramid^2)/4). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Slant Height of Square Pyramid?

Here are the different ways to Calculate Slant Height of Square Pyramid-

Slant Height of Square Pyramid=sqrt((Edge Length of Base of Square Pyramid^2)/4+Height of Square Pyramid^2)

Can the Slant Height of Square Pyramid given Total Surface Area be negative?

No, the Slant Height of Square Pyramid given Total Surface Area, measured in Length cannot be negative.

Which unit is used to measure Slant Height of Square Pyramid given Total Surface Area?

Slant Height of Square Pyramid given Total Surface Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Slant Height of Square Pyramid given Total Surface Area can be measured.

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Slant Height of Square Pyramid given Total Surface Area Formula

​GoSlant Height of Square Pyramid Formula

Slant Height of Square Pyramid given Total Surface Area Example

Slant Height of Square Pyramid given Total Surface Area Solution

Slant Height of Square Pyramid given Total Surface Area Formula Elements

Other Formulas to find Slant Height of Square Pyramid

Other formulas in Slant Height of Square Pyramid category

How to Evaluate Slant Height of Square Pyramid given Total Surface Area?

FAQs on Slant Height of Square Pyramid given Total Surface Area

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GoSlant Height of Square Pyramid Formula