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What is the formula for the area of a scalane triangular prism?

Answer 1

#"Volume" = dsqrt(s(s-a)(s-b)(s-c))#
where #d# is the length of the prism,
#a, b, c# are the lengths of the 3 sides of the scalene triangle,
and #s# is the semi-perimeter of the scalene triangle (i.e. #(a+b+c)/2#)

I assume you meant "volume" and not "area" since a prism is a 3-D construct.

#sqrt(s(s-a)(s-b)(s-c))# is Heron's formula for the area of a triangle with sides #a,b,c#

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Answer 2

Carson Arnold

The formula for the surface area ( A ) of a scalene triangular prism is given by:

[ A = 2 \times (\text{Area of base triangle}) + \text{Perimeter of base triangle} \times (\text{Height of prism}) ]

Where the area of the base triangle is calculated using Heron's formula:

[ \text{Area of base triangle} = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c)} ]

Here, ( a, b, ) and ( c ) are the side lengths of the base triangle, and ( s ) is the semiperimeter of the base triangle given by:

[ s = \frac{a + b + c}{2} ]

The height of the prism is perpendicular to the base triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.