Height of Square Pyramid given Total Surface Area Calculator

✖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%
✖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%

✖Height of Square Pyramid is the length of the perpendicular from the apex to the base of the Square Pyramid.ⓘ Height of Square Pyramid given Total Surface Area [h]

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Height of Square Pyramid given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Square Pyramid = sqrt((((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 = sqrt((((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

Height of Square Pyramid - (Measured in Meter) - Height of Square Pyramid is the length of the perpendicular from the apex to 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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

h = 15.1986841535707

STEP 3: Convert Result to Output's Unit

15.1986841535707 Meter --> No Conversion Required

FINAL ANSWER

15.1986841535707 ≈ 15.19868 Meter <-- Height of Square Pyramid

(Calculation completed in 00.004 seconds)

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< Height of Square Pyramid Calculators

Height of Square Pyramid given Base Angle

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

Height of Square Pyramid given Total Surface Area

LaTeX Go Height of Square Pyramid = sqrt((((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)

Height of Square Pyramid given Lateral Edge Length

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

Height of Square Pyramid given Slant Height

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

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 Height of Square Pyramid given Total Surface Area?

Height of Square Pyramid given Total Surface Area calculator uses Height of Square Pyramid = sqrt((((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 Height of Square Pyramid, Height of Square Pyramid given Total Surface Area formula is defined as the length of the perpendicular from the apex to the base of the Square Pyramid and is calculated using the total surface area of the Square Pyramid. Height of Square Pyramid is denoted by h symbol.

How to calculate Height of Square Pyramid given Total Surface Area using this online calculator? To use this online calculator for Height of Square Pyramid given Total Surface Area, enter Total Surface Area of Square Pyramid (TSA) & Edge Length of Base of Square Pyramid (l_e(Base)) and hit the calculate button. Here is how the Height of Square Pyramid given Total Surface Area calculation can be explained with given input values -> 15.19868 = sqrt((((420-10^2)/10)^2-10^2)/4).

FAQ

What is Height of Square Pyramid given Total Surface Area?

Height of Square Pyramid given Total Surface Area formula is defined as the length of the perpendicular from the apex to the base of the Square Pyramid and is calculated using the total surface area of the Square Pyramid and is represented as h = sqrt((((TSA-l_e(Base)^2)/l_e(Base))^2-l_e(Base)^2)/4) or Height of Square Pyramid = sqrt((((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). Total Surface Area of Square Pyramid is the total amount of two-dimensional space occupied on all the faces of the 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.

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

Height of Square Pyramid given Total Surface Area formula is defined as the length of the perpendicular from the apex to the base of the Square Pyramid and is calculated using the total surface area of the Square Pyramid is calculated using Height of Square Pyramid = sqrt((((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 Height of Square Pyramid given Total Surface Area, you need Total Surface Area of Square Pyramid (TSA) & Edge Length of Base of Square Pyramid (l_e(Base)). With our tool, you need to enter the respective value for Total Surface Area of Square Pyramid & Edge Length of Base 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 Height of Square Pyramid?

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

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

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