Total Surface Area of Square Pyramid given Lateral Edge Length 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%
✖Lateral Edge Length of Square Pyramid is the length of the straight line connecting any base vertex to the apex of the Square Pyramid.ⓘ Lateral Edge Length of Square Pyramid [l_e(Lateral)]			+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 given Lateral Edge Length [TSA]

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Total Surface Area of Square Pyramid given Lateral Edge Length

Formula

`"TSA" = "l"_{"e(Base)"}^2+("l"_{"e(Base)"}*sqrt((4*"l"_{"e(Lateral)"}^2)-"l"_{"e(Base)"}^2))`

Example

`"424.9615m²"=("10m")^2+("10m"*sqrt((4*("17m")^2)-("10m")^2))`

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Total Surface Area of Square Pyramid given Lateral Edge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Square Pyramid = Edge Length of Base of Square Pyramid^2+(Edge Length of Base of Square Pyramid*sqrt((4*Lateral Edge Length of Square Pyramid^2)-Edge Length of Base of Square Pyramid^2))
TSA = l_e(Base)^2+(l_e(Base)*sqrt((4*l_e(Lateral)^2)-l_e(Base)^2))
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

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.
Lateral Edge Length of Square Pyramid - (Measured in Meter) - Lateral Edge Length of Square Pyramid is the length of the straight line connecting any base vertex to the apex 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
Lateral Edge Length of Square Pyramid: 17 Meter --> 17 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = l_e(Base)^2+(l_e(Base)*sqrt((4*l_e(Lateral)^2)-l_e(Base)^2)) --> 10^2+(10*sqrt((4*17^2)-10^2))

Evaluating ... ...

TSA = 424.961536185438

STEP 3: Convert Result to Output's Unit

424.961536185438 Square Meter --> No Conversion Required

FINAL ANSWER

424.961536185438 ≈ 424.9615 Square Meter <-- Total Surface Area of Square Pyramid

(Calculation completed in 00.004 seconds)

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< 8 Surface Area of Square Pyramid Calculators

Total Surface Area of Square Pyramid given Lateral Edge Length and Height

Go Total Surface Area of Square Pyramid = (2*(Lateral Edge Length of Square Pyramid^2-Height of Square Pyramid^2))+ (sqrt(2*(Lateral Edge Length of Square Pyramid^2-Height of Square Pyramid^2))* sqrt(2*(Lateral Edge Length of Square Pyramid^2+Height of Square Pyramid^2)))

Total Surface Area of Square Pyramid given Slant Height and Height

Go Total Surface Area of Square Pyramid = (4*(Slant Height of Square Pyramid^2-Height of Square Pyramid^2))+(4*Slant Height of Square Pyramid*sqrt(Slant Height of Square Pyramid^2-Height of Square Pyramid^2))

Total Surface Area of Square Pyramid given Lateral Edge Length

Go Total Surface Area of Square Pyramid = Edge Length of Base of Square Pyramid^2+(Edge Length of Base of Square Pyramid*sqrt((4*Lateral Edge Length of Square Pyramid^2)-Edge Length of Base of Square Pyramid^2))

Total Surface Area of Square Pyramid

Go Total Surface Area of Square Pyramid = Edge Length of Base of Square Pyramid^2+(Edge Length of Base of Square Pyramid*sqrt((4*Height of Square Pyramid^2)+Edge Length of Base of Square Pyramid^2))

Lateral Surface Area of Square Pyramid

Go Lateral Surface Area of Square Pyramid = 2*Edge Length of Base of Square Pyramid*sqrt((Edge Length of Base of Square Pyramid^2)/4+Height of Square Pyramid^2)

Total Surface Area of Square Pyramid given Slant Height

Go Total Surface Area of Square Pyramid = (2*Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid)+Edge Length of Base of Square Pyramid^2

Lateral Surface Area of Square Pyramid given Slant Height

Go Lateral Surface Area of Square Pyramid = 2*Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid

Base Area of Square Pyramid

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

Total Surface Area of Square Pyramid given Lateral Edge Length Formula

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 Total Surface Area of Square Pyramid given Lateral Edge Length?

Total Surface Area of Square Pyramid given Lateral Edge Length calculator uses Total Surface Area of Square Pyramid = Edge Length of Base of Square Pyramid^2+(Edge Length of Base of Square Pyramid*sqrt((4*Lateral Edge Length of Square Pyramid^2)-Edge Length of Base of Square Pyramid^2)) to calculate the Total Surface Area of Square Pyramid, Total Surface Area of Square Pyramid given Lateral Edge Length formula is defined as the total amount of two-dimensional space occupied on all the faces of the Square Pyramid and is calculated using the lateral edge length of the Square Pyramid. Total Surface Area of Square Pyramid is denoted by TSA symbol.

How to calculate Total Surface Area of Square Pyramid given Lateral Edge Length using this online calculator? To use this online calculator for Total Surface Area of Square Pyramid given Lateral Edge Length, enter Edge Length of Base of Square Pyramid (l_e(Base)) & Lateral Edge Length of Square Pyramid (l_e(Lateral)) and hit the calculate button. Here is how the Total Surface Area of Square Pyramid given Lateral Edge Length calculation can be explained with given input values -> 424.9615 = 10^2+(10*sqrt((4*17^2)-10^2)).

FAQ

What is Total Surface Area of Square Pyramid given Lateral Edge Length?

Total Surface Area of Square Pyramid given Lateral Edge Length formula is defined as the total amount of two-dimensional space occupied on all the faces of the Square Pyramid and is calculated using the lateral edge length of the Square Pyramid and is represented as TSA = l_e(Base)^2+(l_e(Base)*sqrt((4*l_e(Lateral)^2)-l_e(Base)^2)) or Total Surface Area of Square Pyramid = Edge Length of Base of Square Pyramid^2+(Edge Length of Base of Square Pyramid*sqrt((4*Lateral Edge Length of Square Pyramid^2)-Edge Length of Base of Square Pyramid^2)). 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 & Lateral Edge Length of Square Pyramid is the length of the straight line connecting any base vertex to the apex of the Square Pyramid.

How to calculate Total Surface Area of Square Pyramid given Lateral Edge Length?

Total Surface Area of Square Pyramid given Lateral Edge Length formula is defined as the total amount of two-dimensional space occupied on all the faces of the Square Pyramid and is calculated using the lateral edge length of the Square Pyramid is calculated using Total Surface Area of Square Pyramid = Edge Length of Base of Square Pyramid^2+(Edge Length of Base of Square Pyramid*sqrt((4*Lateral Edge Length of Square Pyramid^2)-Edge Length of Base of Square Pyramid^2)). To calculate Total Surface Area of Square Pyramid given Lateral Edge Length, you need Edge Length of Base of Square Pyramid (l_e(Base)) & Lateral Edge Length of Square Pyramid (l_e(Lateral)). With our tool, you need to enter the respective value for Edge Length of Base of Square Pyramid & Lateral Edge Length 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 Total Surface Area of Square Pyramid?

In this formula, Total Surface Area of Square Pyramid uses Edge Length of Base of Square Pyramid & Lateral Edge Length of Square Pyramid. We can use 4 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Square Pyramid = (2*Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid)+Edge Length of Base of Square Pyramid^2
Total Surface Area of Square Pyramid = Edge Length of Base of Square Pyramid^2+(Edge Length of Base of Square Pyramid*sqrt((4*Height of Square Pyramid^2)+Edge Length of Base of Square Pyramid^2))
Total Surface Area of Square Pyramid = (4*(Slant Height of Square Pyramid^2-Height of Square Pyramid^2))+(4*Slant Height of Square Pyramid*sqrt(Slant Height of Square Pyramid^2-Height of Square Pyramid^2))
Total Surface Area of Square Pyramid = (2*(Lateral Edge Length of Square Pyramid^2-Height of Square Pyramid^2))+ (sqrt(2*(Lateral Edge Length of Square Pyramid^2-Height of Square Pyramid^2))* sqrt(2*(Lateral Edge Length of Square Pyramid^2+Height of Square Pyramid^2)))

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