Triangular Prism Calculator

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Triangular Prism Calculator

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Triangular Prism Image

side length a =

side length b =

side length c =

prism height h =

Units

Significant Figures

Answer:

Volume

V =

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Triangular Prism Shape

Triangular Prism Diagram with h = height and side lengths a, b and c

a = side length a
b = side length b = bottom triangle base b
c = side length c
h = height of prism
H = height of bottom triangle
V = volume
A_tot = total surface area = all sides
A_lat = lateral surface area = all rectangular sides
A_top = top surface area = top triangle
A_bot = bottom surface area = bottom triangle

A triangular prism is a geometric solid shape with a triangle as its base. It's a three-sided prism where the base and top are equal triangles and the remaining 3 sides are rectangles.

Calculator Use

This calculator finds the volume, surface area and height of a triangular prism. Surface area calculations include top, bottom, lateral sides and total surface area. Height is calculated from known volume or lateral surface area.

Units: Units are shown for convenience but do not affect calculations. Answers will be the same whether in feet, ft², ft³, or meters, m², m³, or any other unit measure.

Significant Figures: Choose the number of significant figures or leave on auto to let the calculator determine number precision.

Triangular Prism Formulas in terms of height and triangle side lengths a, b and c:

Volume of a Triangular Prism Formula

Finds the 3-dimensional space occupied by a triangular prism.

\[ V = \dfrac{1}{4}h \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} \]

\[ V = \dfrac{1}{4}h \sqrt{\begin{aligned}(a+&b+c)(b+c-a)\\&\times(c+a-b)(a+b-c)\end{aligned}} \]

Top Surface Area of a Triangular Prism Formula

Finds the area contained by the triangular surface at the top of the prism. This is the same area as the bottom surface area.

\[ A_{top} = \dfrac{1}{4} \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} \]

\[ A_{top} = \dfrac{1}{4} \sqrt{\begin{aligned}(a+&b+c)(b+c-a)\\&\times(c+a-b)(a+b-c)\end{aligned}} \]

Bottom Surface Area of a Triangular Prism Formula

Finds the area contained by the triangular surface at the bottom of the prism. This is the same area as the top surface area.

\[ A_{bot} = \dfrac{1}{4} \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} \]

\[ A_{bot} = \dfrac{1}{4} \sqrt{\begin{aligned}(a+&b+c)(b+c-a)\\&\times(c+a-b)(a+b-c)\end{aligned}} \]

Lateral Surface Area of a Triangular Prism Formula

Finds the total area contained by the three rectangular sides of the prism. You can think of the lateral surface area as the total surface area of the prism minus the two triangular areas at the top and bottom of the prism.

\[ A_{lat} = h (a+b+c) \]

Total Surface Area of a Triangular Prism Formula

Finds the total area of all sides of a triangular prism. Total surface area of a prism includes the area of the top and bottom triangle sides of the prism, plus the area of all 3 rectangular sides.

\[ A_{tot} = A_{top} + A_{bot} + A_{lat} \]

Height of a Triangular Prism Formula in Terms of Volume

Finds the height of a triangular prism by solving the Volume Formula for height. Height, h, is calculated from volume, V, and side lengths a, b and c.

\[ h = \dfrac{4V}{\sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}} \]

\[ h = 4V \div \sqrt{\begin{aligned}(a+&b+c)(b+c-a)\\&\times(c+a-b)(a+b-c)\end{aligned}} \]

Height of a Triangular Prism Formula in Terms of Lateral Surface Area

Finds the height of a triangular prism by solving the Lateral Surface Area Formula for height. Height, h, is calculated from lateral surface area, A_lat, and side lengths a, b and c.

\[ h = \dfrac{A_{lat}}{(a+b+c)} \]

Reference

Weisstein, Eric W. "Triangle Area." From MathWorld--A Wolfram Web Resource, Triangle Area.