Slant Height of Square Pyramid given Total Surface Area Calculator

✖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.ⓘ Edge Length of Base of Square Pyramid [l_e(Base)]			+10% -10%
✖Total Surface Area of Square Pyramid is the total amount of two-dimensional space occupied on all the faces of the Square Pyramid.ⓘ Total Surface Area of Square Pyramid [TSA]			+10% -10%

✖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.ⓘ Slant Height of Square Pyramid given Total Surface Area [h_slant]

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Slant Height of Square Pyramid given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
h_slant = sqrt((l_e(Base)^2)/4+(((TSA-l_e(Base)^2)/l_e(Base))^2-l_e(Base)^2)/4)
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

Slant Height of Square Pyramid - (Measured in Meter) - 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.
Edge Length of Base of Square Pyramid - (Measured in Meter) - 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.
Total Surface Area of Square Pyramid - (Measured in Square Meter) - Total Surface Area of Square Pyramid is the total amount of two-dimensional space occupied on all the faces of the Square Pyramid.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Base of Square Pyramid: 10 Meter --> 10 Meter No Conversion Required
Total Surface Area of Square Pyramid: 420 Square Meter --> 420 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_slant = sqrt((l_e(Base)^2)/4+(((TSA-l_e(Base)^2)/l_e(Base))^2-l_e(Base)^2)/4) --> sqrt((10^2)/4+(((420-10^2)/10)^2-10^2)/4)

Evaluating ... ...

h_slant = 16

STEP 3: Convert Result to Output's Unit

16 Meter --> No Conversion Required

FINAL ANSWER

16 Meter <-- Slant Height of Square Pyramid

(Calculation completed in 00.008 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< Slant Height of Square Pyramid Calculators

Slant Height of Square Pyramid given Total Surface Area

LaTeX Go 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)

Slant Height of Square Pyramid given Lateral Edge Length and Height

LaTeX Go Slant Height of Square Pyramid = sqrt(Height of Square Pyramid^2+(Lateral Edge Length of Square Pyramid^2-Height of Square Pyramid^2)/2)

Slant Height of Square Pyramid given Lateral Edge Length

LaTeX Go Slant Height of Square Pyramid = sqrt(Lateral Edge Length of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4)

Slant Height of Square Pyramid

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

< Important Formulas of Regular Square Pyramid Calculators

Base Angle of Square Pyramid

LaTeX Go Base Angle of Square Pyramid = arccos(((Edge Length of Base of Square Pyramid/2)^2+Slant Height of Square Pyramid^2-Height of Square Pyramid^2)/(Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid))

Lateral Edge Length of Square Pyramid

LaTeX Go Lateral Edge Length of Square Pyramid = sqrt(Edge Length of Base of Square Pyramid^2/2+Height of Square Pyramid^2)

Slant Height of Square Pyramid

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

Base Area of Square Pyramid

LaTeX Go Base Area of Square Pyramid = Edge Length of Base of Square Pyramid^2

Slant Height of Square Pyramid given Total Surface Area Formula

LaTeX Go

What is a Square Pyramid?

A Square Pyramid is a pyramid with a square base and four isosceles triangular faces that intersect at a point in geometry (the apex). It has 5 faces, which include 4 isosceles triangular faces, and a square base. Also, It has 5 vertices and 8 edges.

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

Slant Height of Square Pyramid given Total Surface Area calculator 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 calculate 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 calculate Slant Height of Square Pyramid given Total Surface Area using this online calculator? To use this online calculator 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. Here is how the Slant Height of Square Pyramid given Total Surface Area calculation can be explained with given input values -> 16 = sqrt((10^2)/4+(((420-10^2)/10)^2-10^2)/4).

FAQ

What is Slant Height of Square Pyramid given Total Surface Area?

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 and is represented as h_slant = sqrt((l_e(Base)^2)/4+(((TSA-l_e(Base)^2)/l_e(Base))^2-l_e(Base)^2)/4) or 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). 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 & Total Surface Area of Square Pyramid is the total amount of two-dimensional space occupied on all the faces of the Square Pyramid.

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

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 is calculated using 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 calculate Slant Height of Square Pyramid given Total Surface Area, you need Edge Length of Base of Square Pyramid (l_e(Base)) & Total Surface Area of Square Pyramid (TSA). With our tool, you need to enter the respective value for Edge Length of Base of Square Pyramid & Total Surface Area of Square 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 Slant Height of Square Pyramid?

In this formula, Slant Height of Square Pyramid uses Edge Length of Base of Square Pyramid & Total Surface Area of Square Pyramid. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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