Question

I need help solving the volume of these triangular prisms.

Answer 1

Volume of a triangular prism:

`(1)/(2)b* h* H`

Where:

b = 10m

H = 4m

h = ?

To find h, we use the formula:

`h\text{ = }(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{ =}(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{ = }(1)/(2)*10*4.8*4\text{ = 96}`

V = 96 m³