Triangular prism

The base of the perpendicular triangular prism is a right triangle with a leg length of 5 cm. The area of the largest sidewall of its surface is 130 cm², and the body's height is 10 cm. Calculate its volume.

Correct answer:

V =  300 cm³

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ h=10\text{cm} \\ S=130{\text{cm}}^2 \\ c=S/h=130/10=13\text{cm} \\ b=\sqrt{c^2-a^2}=\sqrt{13^2-5^2}=12\text{cm} \\ {S}_2=a\cdot b/2=5\cdot 12/2=30{\text{cm}}^2 \\ V=S_2\cdot h=30\cdot 10=300{\text{cm}}^3 \end{gathered}$$

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