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Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s) Solution

STEP 0: Pre-Calculation Summary
Formula Used
height = sqrt((Slant Height^2)-((Side A^2)/4))
h = sqrt((s^2)-((a^2)/4))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Slant Height - Slant Height is the height of a cone from the vertex to the periphery (rather than the center) of the base. (Measured in Meter)
Side A - Side A is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Slant Height: 5 Meter --> 5 Meter No Conversion Required
Side A: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = sqrt((s^2)-((a^2)/4)) --> sqrt((5^2)-((8^2)/4))
Evaluating ... ...
h = 3
STEP 3: Convert Result to Output's Unit
3 Meter --> No Conversion Required
FINAL ANSWER
3 Meter <-- Height
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Area of a Triangle when sides are given
area = sqrt((Side A+Side B+Side C)*(Side B+Side C-Side A)*(Side A-Side B+Side C)*(Side A+Side B-Side C))/4 Go
Radius of Inscribed Circle
radius_of_inscribed_circle = sqrt((Semiperimeter Of Triangle-Side A)*(Semiperimeter Of Triangle-Side B)*(Semiperimeter Of Triangle-Side C)/Semiperimeter Of Triangle) Go
Area of Triangle when semiperimeter is given
area_of_triangle = sqrt(Semiperimeter Of Triangle*(Semiperimeter Of Triangle-Side A)*(Semiperimeter Of Triangle-Side B)*(Semiperimeter Of Triangle-Side C)) Go
side b of a triangle
side_b = sqrt(Side A^2+Side C^2-2*Side A*Side C*cos(Angle B)) Go
Perimeter of a Right Angled Triangle
perimeter = Side A+Side B+sqrt(Side A^2+Side B^2) Go
Radius of circumscribed circle
radius_of_circumscribed_circle = (Side A*Side B*Side C)/(4*Area Of Triangle) Go
Perimeter of Triangle
perimeter_of_triangle = Side A+Side B+Side C Go
Perimeter of a Parallelogram
perimeter = 2*Side A+2*Side B Go
Perimeter of a Kite
perimeter = 2*(Side A+Side B) Go
Perimeter of an Isosceles Triangle
perimeter = Side A+2*Side B Go
Area of a Square when side is given
area = (Side A)^2 Go

11 Other formulas that calculate the same Output

Height of a triangular prism when lateral surface area is given
height = Lateral Surface Area/(Side A+Side B+Side C) Go
Height of an isosceles trapezoid
height = sqrt(Side C^2-0.25*(Side A-Side B)^2) Go
Altitude of an isosceles triangle
height = sqrt((Side A)^2+((Side B)^2/4)) Go
Height of a triangular prism when base and volume are given
height = (2*Volume)/(Base*Length) Go
Height of a trapezoid when area and sum of parallel sides are given
height = (2*Area)/Sum of parallel sides of a trapezoid Go
Altitude of the largest right pyramid with a square base that can be inscribed in a sphere of radius a
height = 4*Radius of Sphere/3 Go
Height of Cone inscribed in a sphere for maximum volume of cone in terms of radius of sphere
height = 4*Radius of Sphere/3 Go
Height of Cone circumscribing a sphere such that volume of cone is minimum
height = 4*Radius of Sphere Go
Height of parabolic section that can be cut from a cone for maximum area of parabolic section
height = 0.75*Slant Height Go
Height of a circular cylinder of maximum convex surface area in a given circular cone
height = Height of Cone/2 Go
Height of Largest right circular cylinder that can be inscribed within a cone
height = Height of Cone/3 Go

Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s) Formula

height = sqrt((Slant Height^2)-((Side A^2)/4))
h = sqrt((s^2)-((a^2)/4))

What is Square Pyramid?

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has C4v symmetry. If all edges are equal, it is an equilateral square pyramid, the Johnson solid J1.

How to Calculate Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s)?

Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s) calculator uses height = sqrt((Slant Height^2)-((Side A^2)/4)) to calculate the Height, Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s) formula is defined as the measurement of Square Pyramid from head to foot or from base to top. Height and is denoted by h symbol.

How to calculate Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s) using this online calculator? To use this online calculator for Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s), enter Slant Height (s) and Side A (a) and hit the calculate button. Here is how the Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s) calculation can be explained with given input values -> 3 = sqrt((5^2)-((8^2)/4)).

FAQ

What is Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s)?
Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s) formula is defined as the measurement of Square Pyramid from head to foot or from base to top and is represented as h = sqrt((s^2)-((a^2)/4)) or height = sqrt((Slant Height^2)-((Side A^2)/4)). Slant Height is the height of a cone from the vertex to the periphery (rather than the center) of the base and Side A is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.
How to calculate Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s)?
Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s) formula is defined as the measurement of Square Pyramid from head to foot or from base to top is calculated using height = sqrt((Slant Height^2)-((Side A^2)/4)). To calculate Height (h) of Square Pyramid given Edge length of the base (a) and Slant height (s), you need Slant Height (s) and Side A (a). With our tool, you need to enter the respective value for Slant Height and Side A 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?
In this formula, Height uses Slant Height and Side A. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • height = 4*Radius of Sphere/3
  • height = 4*Radius of Sphere
  • height = Height of Cone/3
  • height = 4*Radius of Sphere/3
  • height = Height of Cone/2
  • height = 0.75*Slant Height
  • height = sqrt(Side C^2-0.25*(Side A-Side B)^2)
  • height = (2*Area)/Sum of parallel sides of a trapezoid
  • height = sqrt((Side A)^2+((Side B)^2/4))
  • height = (2*Volume)/(Base*Length)
  • height = Lateral Surface Area/(Side A+Side B+Side C)
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