# Prism

The base of a perpendicular 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?

Result

S =  99 cm2

#### Solution:

$a=4.5 \ \text{cm} \ \\ b=6 \ \text{cm} \ \\ \ \\ S_{1}=a \cdot \ b / 2=4.5 \cdot \ 6 / 2=\dfrac{ 27 }{ 2 }=13.5 \ \text{cm}^2 \ \\ V=54 \ \text{cm}^3 \ \\ h=V / S_{1}=54 / 13.5=4 \ \text{cm} \ \\ \ \\ c=\sqrt{ a^2+b^2 }=\sqrt{ 4.5^2+6^2 }=\dfrac{ 15 }{ 2 }=7.5 \ \\ S=2 \cdot \ S_{1} + (a+b+c) \cdot \ h=2 \cdot \ 13.5 + (4.5+6+7.5) \cdot \ 4=99 \ \text{cm}^2$

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