Total Surface Area of Hollow Pyramid Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2)))
TSA = n*le(Base)/2*(sqrt(hTotal^2+(le(Base)^2/4*(cot(pi/n))^2))+sqrt(hMissing^2+(le(Base)^2/4*(cot(pi/n))^2)))
This formula uses 1 Constants, 2 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)
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 Hollow Pyramid - (Measured in Square Meter) - Total Surface Area of Hollow Pyramid is the total amount of two-dimensional space occupied by all the faces of the Hollow Pyramid.
Number of Base Vertices of Hollow Pyramid - Number of Base Vertices of Hollow Pyramid are the number of base vertices of a regular Hollow Pyramid.
Edge Length of Base of Hollow Pyramid - (Measured in Meter) - Edge Length of Base of Hollow Pyramid is the length of the straight line connecting any two adjacent vertices on the base of the Hollow Pyramid.
Total Height of Hollow Pyramid - (Measured in Meter) - Total Height of Hollow Pyramid is the total length of the perpendicular from the apex to the base of the complete pyramid in the Hollow Pyramid.
Missing Height of Hollow Pyramid - (Measured in Meter) - Missing Height of Hollow Pyramid is the length of the perpendicular from the apex of the removed pyramid to the base of the removed pyramid in the Hollow Pyramid.
STEP 1: Convert Input(s) to Base Unit
Number of Base Vertices of Hollow Pyramid: 4 --> No Conversion Required
Edge Length of Base of Hollow Pyramid: 10 Meter --> 10 Meter No Conversion Required
Total Height of Hollow Pyramid: 15 Meter --> 15 Meter No Conversion Required
Missing Height of Hollow Pyramid: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = n*le(Base)/2*(sqrt(hTotal^2+(le(Base)^2/4*(cot(pi/n))^2))+sqrt(hMissing^2+(le(Base)^2/4*(cot(pi/n))^2))) --> 4*10/2*(sqrt(15^2+(10^2/4*(cot(pi/4))^2))+sqrt(7^2+(10^2/4*(cot(pi/4))^2)))
Evaluating ... ...
TSA = 488.27427135769
STEP 3: Convert Result to Output's Unit
488.27427135769 Square Meter --> No Conversion Required
FINAL ANSWER
488.27427135769 488.2743 Square Meter <-- Total Surface Area of Hollow Pyramid
(Calculation completed in 00.004 seconds)

Credits

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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3 Surface Area of Hollow Pyramid Calculators

Total Surface Area of Hollow Pyramid given Inner Height and Missing Height
Go Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt((Inner Height of Hollow Pyramid+Missing Height of Hollow Pyramid)^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2)))
Total Surface Area of Hollow Pyramid given Inner Height and Total Height
Go Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt((Total Height of Hollow Pyramid-Inner Height of Hollow Pyramid)^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2)))
Total Surface Area of Hollow Pyramid
Go Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2)))

Total Surface Area of Hollow Pyramid Formula

Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2)))
TSA = n*le(Base)/2*(sqrt(hTotal^2+(le(Base)^2/4*(cot(pi/n))^2))+sqrt(hMissing^2+(le(Base)^2/4*(cot(pi/n))^2)))

What is a Hollow Pyramid?

A Hollow Pyramid is a regular pyramid, of which another regular pyramid with the same base and lesser height is removed at its base and is concave. An N-sided polygon as the base of the pyramid, It has 2N isosceles triangular faces. Also, It has N+2 vertices and 3N edges.

How to Calculate Total Surface Area of Hollow Pyramid?

Total Surface Area of Hollow Pyramid calculator uses Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))) to calculate the Total Surface Area of Hollow Pyramid, Total Surface Area of Hollow Pyramid formula is defined as the total amount of two-dimensional space occupied by all the faces of the Hollow Pyramid. Total Surface Area of Hollow Pyramid is denoted by TSA symbol.

How to calculate Total Surface Area of Hollow Pyramid using this online calculator? To use this online calculator for Total Surface Area of Hollow Pyramid, enter Number of Base Vertices of Hollow Pyramid (n), Edge Length of Base of Hollow Pyramid (le(Base)), Total Height of Hollow Pyramid (hTotal) & Missing Height of Hollow Pyramid (hMissing) and hit the calculate button. Here is how the Total Surface Area of Hollow Pyramid calculation can be explained with given input values -> 488.2743 = 4*10/2*(sqrt(15^2+(10^2/4*(cot(pi/4))^2))+sqrt(7^2+(10^2/4*(cot(pi/4))^2))).

FAQ

What is Total Surface Area of Hollow Pyramid?
Total Surface Area of Hollow Pyramid formula is defined as the total amount of two-dimensional space occupied by all the faces of the Hollow Pyramid and is represented as TSA = n*le(Base)/2*(sqrt(hTotal^2+(le(Base)^2/4*(cot(pi/n))^2))+sqrt(hMissing^2+(le(Base)^2/4*(cot(pi/n))^2))) or Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))). Number of Base Vertices of Hollow Pyramid are the number of base vertices of a regular Hollow Pyramid, Edge Length of Base of Hollow Pyramid is the length of the straight line connecting any two adjacent vertices on the base of the Hollow Pyramid, Total Height of Hollow Pyramid is the total length of the perpendicular from the apex to the base of the complete pyramid in the Hollow Pyramid & Missing Height of Hollow Pyramid is the length of the perpendicular from the apex of the removed pyramid to the base of the removed pyramid in the Hollow Pyramid.
How to calculate Total Surface Area of Hollow Pyramid?
Total Surface Area of Hollow Pyramid formula is defined as the total amount of two-dimensional space occupied by all the faces of the Hollow Pyramid is calculated using Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))). To calculate Total Surface Area of Hollow Pyramid, you need Number of Base Vertices of Hollow Pyramid (n), Edge Length of Base of Hollow Pyramid (le(Base)), Total Height of Hollow Pyramid (hTotal) & Missing Height of Hollow Pyramid (hMissing). With our tool, you need to enter the respective value for Number of Base Vertices of Hollow Pyramid, Edge Length of Base of Hollow Pyramid, Total Height of Hollow Pyramid & Missing Height of Hollow 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 Hollow Pyramid?
In this formula, Total Surface Area of Hollow Pyramid uses Number of Base Vertices of Hollow Pyramid, Edge Length of Base of Hollow Pyramid, Total Height of Hollow Pyramid & Missing Height of Hollow Pyramid. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt((Inner Height of Hollow Pyramid+Missing Height of Hollow Pyramid)^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2)))
  • Total Surface Area of Hollow Pyramid = Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt((Total Height of Hollow Pyramid-Inner Height of Hollow Pyramid)^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2)))
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