Triangular Prism Height Calculator

Find the height of an equilateral triangular prism from its side length and volume. Also shows base area, lateral area, and total surface area.

Input

For a triangular prism with an equilateral base, find the height from the side length and volume. Base area, lateral area, and surface area are also calculated.

Side a

Volume V

Result

Height h

7.698004

Base area

15.588457

Lateral area

138.564065

Surface area

169.740979

Lengths use the same unit as the input. Area is squared and volume is cubed.

How it works

The base is an equilateral triangle with side a, and the base area is (sqrt 3 over 4) times a squared.
The height h is the volume V divided by the base area, so h = V over base area.
The lateral area is the base perimeter 3a multiplied by the height h, giving 3 times a times h.
The total surface area is the two bases plus the lateral area, equal to 2 times the base area plus the lateral area.
Enter a positive side length and a positive volume. Length units are shared, while area is squared and volume is cubed.

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