Perpendicular prism network

Find the volume and surface of a triangular prism with the base of a right triangle, the network of which is 4 cm 3 cm (perpendiculars) and nine centimeters (height of the prism).

Correct answer:

V =  54 cm³
S =  120 cm²

Step-by-step explanation:

$$\begin{gathered} a=4\text{cm} \\ b=3\text{cm} \\ h=9\text{cm} \\ c=\sqrt{a^2+b^2}=\sqrt{4^2+3^2}=5\text{cm} \\ {S}_1=a\cdot b/2=4\cdot 3/2=6{\text{cm}}^2 \\ V=S_1\cdot h=6\cdot 9=54{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} o=a+b+c=4+3+5=12\text{cm} \\ S=2\cdot S_1+o\cdot h=2\cdot 6+12\cdot 9=120{\text{cm}}^2 \end{gathered}$$

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