# Volume of a Triangular Prism Formula

## Volume of a Triangular Prism Formulas – Definition & Examples

Calculating the Volume of a Triangular Prism
A prism is a solid object that has two congruent faces on either end joined by parallelogram faces laterally. A right prism has rectangular faces instead of parallelogram ones. Both these types of prisms have the same formula for volume. The following diagram shows a right triangular prism and its dimensions.

The volume of any prism is equal to the product of its cross section (base) area and its height (length).
$V = BA \times l$
In the case of a triangular prism, the base area is the area of the triangular base, which can be calculated using Heronâ€™s formula (if the lengths of the sides of the triangle are known) or by using the standard area of a triangle formula (if the lengths of a side of the triangle and its corresponding altitude are known).
$BA = \sqrt{s(s-a)(s-b)(s-c)}$
$s = \frac{(a+b+c)}{2}$
We must always take care of the units of measurement in mathematics. For example, if we want the volume inÂ m3, then we need to calculate the base area in ${m^2}$ and the length in $m$.
Letâ€™s look at an example to see how to use the formula!
Question:Â A prism has triangular ends whose sides areÂ 3Â cmÂ ,Â 4Â cmÂ andÂ 5Â cmÂ .If its volume is 84Â cm3 then find its length.
Solution:
a = 3cm, b = 4cm, c = 5cm
sÃ‚Â  = $\frac{(a+b+c)}{2}$ = $\frac{(3+4+5)}{2}$ = $\frac{12}{2}$ = 6cm
$BA = \sqrt{s(s-a)(s-b)(s-c)}$
Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â =Ã‚Â  $\sqrt{6(6-3)(6-4)(6-5)}$
Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â Ã‚Â =Ã‚Â  $\sqrt{6 Ã— 3 Ã— 2 Ã— 1}$ = $\sqrt{36}$ = $6cm^{2}$
$l = \frac{V}{BA}$ = $\frac{84cm^{3}}{6cm^{2}} = 14cm$

Why donâ€™t you try to solving a problem yourself to see if you have mastered the formula!
Question:Â A triangular prism is such that one of the sides of its triangular faces and its corresponding height are equal in length (sayÂ x cm). The length and the volume of the prism are respectively equal toÂ 10Â cmÂ andÂ 80Â cm3. Find the value ofÂ x.
Options:
(a) 6Â cm
(b) 4Â cm
(c) 8Â cm
(d) none of theseÃ‚
$BA = \binom{1}{2} Ã— x Ã— x = \frac{x^{2}}{2}$
BA = $\frac{V}{l}$
$\frac{x^{2}}{2}$ = $\frac{80}{10}$ = 8
$x^{2}$ = 16