Free · Algebra and geometric relations

Centered Rectangular Pyramid Measures

Relate the height, volume, face slants and surface areas of a right rectangular pyramid.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked example, Base surface area (A_b) = 48, Volume (V) = 192, Lateral edge (d) = 13.

V=lwh/3; edge²=h²+(l²+w²)/4

Worked example

Enter these known values and leave the other values blank.

Base length (a)
6 cm
Base width (b)
8 cm
Pyramid height (H)
12 cm
Base surface area (A_b)
48 cm²
Lateral edge (d)
13 cm
Lateral surface area (A_l)
174.85 cm²
Total surface area (A)
222.85 cm²
Volume (V)
192 cm³
Base diagonal
10 cm
First slant height
12.65 cm
Second slant height
12.37 cm
First lateral face area
37.95 cm²
Second lateral face area
49.48 cm²

Assumptions and limitations

  • The apex lies above the rectangle center and height is perpendicular. All lengths are positive.
  • Face slant for the length edge uses half the width; face slant for the width edge uses half the length.

Common questions

How do I use this relation?

Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.

What do the displayed numbers mean?

The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.

References

Bookify validates the real geometric or algebraic domain and inverse branches omitted or approximated by this capture. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor.

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