What is the surface area of a prism if the volume is 5?
you cant find the area anyways but just to show you that you cant : let h be the height of the prism and b be the breadth of the triangle side of the prism and l be the length of th prism we get [1/2]bhl=5 =>bhl=10 now let me remind you that here there are three variables and we have only one equation [we need 3 eqs] but since we have only one equation lets assume that all sides of the prism are equal suppose b then we have volume of prism as area of triangle side * length => √[3b/2*b/2*b/2*b/2] *b =10 =>b²√3/4 * b=10 =>b³√3=40………………………..… now surface area A would be area of triangle +3b² =>A=b²√3/4 + 3b² =>A=[[12+√3]/4] b² ………………………………….… now we have to substitute b ‘s value from equation 1 =>A=[[12+√3]/4]*cube root of [40/√3] =>A=[[12+1.732]/4] * cube root of [40/1.732] =>A=[13.732/4] * cube root of 23.0946 =>A=3.433 * 2.84776 =>A=9.7763 I hope you got your answer
