How To Find Height With Slant Height

Pyramid Estimator

Choose a Calculation

Units

Meaning Figures

Square Pyramid Shape

h = acme
s = slant top
a = side length
P = perimeter of base
east = lateral edge length
r = a/2
Five = book
L = lateral area
B = base surface expanse
A = full area

Figurer Utilise

This online calculator will summate the diverse backdrop of a square pyramid given 2 known variables. The square pyramid is a special case of a pyramid where the base is square. It is a regular pyramid with a foursquare base of operations.

Units: Note that units are shown for convenience simply practise not affect the calculations. The units are in identify to requite an indication of the guild of the results such as ft, ft^two or ft^three. For example, if you are starting with mm and you know r and h in mm, your calculations will result with due south in mm, Five in mm^three, L in mmⁱⁱ, B in mm² and A in mm².

NAN: means not a number. This will bear witness as a result if you are using values that just exercise not make sense as reasonable values for a pyramid.

Below are the standard formulas for a pyramid. Calculations are based on algebraic manipulation of these standard formulas.

Square Pyramid Formulas derived in terms of side length a and top h:

• Volume of a square pyramid:
  • 5 = (1/3)a²h
• Slant Height of a square pyramid:
  • By the pythagorean theorem we know that
  • s^two = r^two + h²
  • since r = a/2
  • south² = (ane/4)aⁱⁱ + h², and
  • s = √(h² + (1/iv)a²)
  • This is also the height of a triangle side
• Lateral Surface Area of a square pyramid (iv isosceles triangles):
  • For the isosceles triangle Area = (1/2)Base ten Height. Our base is side length a and for this calculation our height for the triangle is slant acme south. With 4 sides we demand to multiply by 4.
  • L = iv x (ane/two)as = 2as = 2a√(h² + (ane/4)a²)
  • Squaring the two to get information technology dorsum within the radical,
  • L = a√(a² + 4h²)
• Base Surface Area of a square pyramid (square):
  • B = a^two
• Total Surface Area of a square pyramid:
  • A = L + B = a^two + a√(a^two + 4h^two))
  • A = a(a + √(a² + 4h²))

Square Pyramid Calculations:

Other formulas for calculations are derived from the formulas in a higher place.

References

Weisstein, Eric W. "Square Pyramid." From MathWorld--A Wolfram Web Resource. Foursquare Pyramid.

Source: https://www.calculatorsoup.com/calculators/geometry-solids/pyramid.php

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