Triangular prism

The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.

Final Answer:

V =  432 cm³
S =  480 cm²

Step-by-step explanation:

$$\begin{gathered} c=10\text{cm} \\ a=8\text{cm} \\ b=\sqrt{c^2-a^2}=\sqrt{10^2-8^2}=6\text{cm} \\ o=a+b+c=8+6+10=24\text{cm} \\ w=75\%=\frac{75}{100}=\frac{3}{4}=0.75 \\ h=w\cdot o=0.75\cdot 24=18\text{cm} \\ {S}_1=\frac{a\cdot b}{2}=\frac{8\cdot 6}{2}=24{\text{cm}}^2 \\ V=S_1\cdot h=24\cdot 18=432{\text{cm}}^3 \end{gathered}$$

$S=2\cdot S_1+o\cdot h=2\cdot 24+24\cdot 18=480{\text{cm}}^2$

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