Prism

The base of a vertical triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism if its volume is 54 cubic centimeters?

Correct answer:

S =  99 cm²

Step-by-step explanation:

$$\begin{gathered} a=4.5\text{cm} \\ b=6\text{cm} \\ {S}_1=a\cdot b/2=4.5\cdot 6/2=\frac{27}{2}=13.5{\text{cm}}^2 \\ V=54{\text{cm}}^3 \\ h=V/S_1=54/13.5=4\text{cm} \\ c=\sqrt{a^2+b^2}=\sqrt{4.5^2+6^2}=\frac{15}{2}=7.5 \\ S=2\cdot S_1+(a+b+c)\cdot h=2\cdot 13.5+(4.5+6+7.5)\cdot 4=99{\text{cm}}^2 \end{gathered}$$

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