Triangular 6345

Calculate the volume and surface of a triangular prism whose base is a right triangle with sides a = 3m, b = Va = 4m, and c = 5m. The height of the prism is v = 5.5 m.

Correct answer:

V =  33 m³
S =  78 m²

Step-by-step explanation:

$$\begin{gathered} a=3\text{m} \\ b=4\text{m} \\ c=5\text{m} \\ h=5.5\text{m} \\ {S}_1=a\cdot b/2=3\cdot 4/2=6{\text{m}}^2 \\ V=S_1\cdot h=6\cdot 5.5=33{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} o=a+b+c=3+4+5=12\text{m} \\ {S}_2=o\cdot h=12\cdot 5.5=66{\text{m}}^2 \\ S=2\cdot S_1+S_2=2\cdot 6+66=78{\text{m}}^2 \end{gathered}$$

Try another example