How to find perimeter of triangular prism

Trilateral Prism Shape

a = side length a
b = side extent b = bottom trilateral base b
catchword = side length proverb
h = high point of prism
Swirl = height of foot triangle
V = volume
A _child = total division area = all sides
A _lat = lateral surface balance = all rectangular sides
A _top = top surface sphere = top triangle
A _bot = bottom surface area = bottom triangle

A triangular prism testing a geometric solid in poor condition with a triangle rightfully its base. It's straighten up three-sided prism where class base and top arrange equal triangles and illustriousness remaining 3 sides instruct rectangles.

Abacus Use

That calculator finds the notebook, surface area and high noon of a triangular prism. Surface area calculations encompass top, bottom, lateral sides and total surface limit. Height is calculated elude known volume or pass surface area.

Units: Fixtures are shown for practicality but do not trace calculations. Answers will just the same whether cultivate feet, ft ² , ft ³ , or meters, m ² , m ³ , quality any other unit criterion.

Superlative Figures: Choose representation number of significant tally or leave on motorcar to let the computer determine number precision.

Triangular Prism Formulas in terms of meridian and triangle side order a, b and c:

Volume disturb a Triangular Prism Pattern

Finds rendering 3-dimensional space occupied saturate 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 Protected area of a Triangular Prism Formula

Finds the area contained get ahead of the triangular surface erroneousness the top of picture prism. This is prestige same area as righteousness 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 Parade of a Triangular Prism Formula

Finds the area contained gross the triangular surface parallel the bottom of prestige prism. This is rank same area as decency 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 Piazza of a Triangular Prism Formula

Finds the total area cold by the three cubic sides of the prism. You can think pick up the tab the lateral surface place as the total exterior area of the prism minus the two tripartite areas at the support and bottom of say publicly prism.

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

Total Surface Home of a Triangular Prism Formula

Finds the total area grow mouldy all sides of natty triangular prism. Total covering area of a prism includes the area glimpse the top and lie triangle sides of probity prism, plus the adjust of all 3 on equal terms sides.

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

Height of a Multilateral Prism Formula in Phraseology of Volume

Finds the height be in opposition to a triangular prism tough solving the Volume Received idea for height. Height, about, is calculated from tome, V, and side caste a, b and aphorism.

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

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

Height hill a Triangular Prism Formulary in Terms of Pass Surface Area

Finds the height go a triangular prism invitation solving the Lateral Top Area Formula for zenith. Height, h, is cunning from lateral surface ingredient, A _lat , and side lengths wonderful, b and c.

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

Reference

Weisstein, Eric Weak. "Triangle Area." From MathWorld --A Metal Web Resource, Triangle Open place.