Right-angled 6034

A three-sided prism has a base in the shape of a right-angled triangle with a length of 5 cm. The giant wall of the prism shell has a volume of 104 cm². The prism is 8 cm high. Calculate the volume and surface area of ​​the prism.

Correct answer:

V =  240 cm³
S =  300 cm²

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ h=8\text{cm} \\ {S}_1=104{\text{cm}}^2 \\ c=S_1/h=104/8=13\text{cm} \\ b=\sqrt{c^2-a^2}=\sqrt{13^2-5^2}=12\text{cm} \\ {S}_2=a\cdot b/2=5\cdot 12/2=30{\text{cm}}^2 \\ V=S_2\cdot h=30\cdot 8=240{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_3=(a+b+c)\cdot h=(5+12+13)\cdot 8=240{\text{cm}}^2 \\ S=2\cdot S_2+S_3=2\cdot 30+240=300{\text{cm}}^2 \end{gathered}$$

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