Triangular prism

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

Correct result:

V =  300 cm³

Solution:

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

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