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 cm b=6 cm  S1=a b/2=4.5 6/2=272=13.5 cm2 V=54 cm3 h=V/S1=54/13.5=4 cm  c=a2+b2=4.52+62=152=7.5 S=2 S1+(a+b+c) h=2 13.5+(4.5+6+7.5) 4=99 cm2a=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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