Question

I need help solving the volume of these triangular prisms.

Answer 1

Volume of a triangular prism:

$\frac{1}{2}b\times h\times H$

Where:

b = 10m

H = 4m

h = ?

To find h, we use the formula:

$h\text{ = }\frac{2}{a}\sqrt[]{S(S\text{ - a)(S - b)(S - c)}}$

Where:

a, b, and c = the lengths of the sides of the triangle.

S is the semiperimeter, which is equal to S = (a + b + c)/2

So:

$\begin{gathered} h\text{ =}\frac{2}{10}\sqrt[]{12(12-10)(12-6)(12-8)} \\ h\text{ = }4.8\text{ m} \end{gathered}$

Now with h, we can use the firs formula to find volume, as follows:

$V\text{ = }\frac{1}{2}\times10\times4.8\times4\text{ = 96}$

V = 96 m³