Triangular prism

The base perpendicular triangular prism is a right triangle whose hypotenuse measures 14 cm and one cathetus 9 cm. The height of the prism is equal to 2/9 of the base's perimeter. Calculate the surface area of the prism.

Correct answer:

S =  349.2 cm²

Step-by-step explanation:

$$\begin{gathered} a=9\text{cm} \\ c=14\text{cm} \\ r=2/9=\frac{2}{9}\doteq 0.2222 \\ {c}^2=a^2+b^2 \\ b=\sqrt{c^2-a^2}=\sqrt{14^2-9^2}=\sqrt{115}\text{cm}\doteq 10.7238\text{cm} \\ o=a+b+c=9+10.7238+14\doteq 33.7238\text{cm} \\ h=r\cdot o=0.2222\cdot 33.7238\doteq 7.4942\text{cm} \\ {S}_1=\frac{a\cdot b}{2}=\frac{9\cdot 10.7238}{2}\doteq 48.2571{\text{cm}}^2 \\ {S}_2=o\cdot h=33.7238\cdot 7.4942\doteq 252.7322{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 48.2571+252.7322=349.2{\text{cm}}^2 \end{gathered}$$

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