Triangular prism

The perpendicular triangular prism is a right triangle with a 5 cm leg. The prism's largest wall area is 130 cm², and the body height is 10 cm. Calculate the body volume.

Correct answer:

V =  300 cm³

Step-by-step explanation:

$$\begin{gathered} a=5 \\ h=10 \\ {S}_3=130 \\ c=S_3/h=130/10=13 \\ b=\sqrt{c^2-a^2}=\sqrt{13^2-5^2}=12 \\ S=a\cdot b/2=5\cdot 12/2=30 \\ V=S\cdot h=30\cdot 10=300{\text{cm}}^3 \end{gathered}$$

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