Answer:
The area of the triangule is 0.77A
Step-by-step explanation:
Given the area, we can calculate one side of the square, the area of a square is height*width, but in this case both are the same so we can say that the area is [tex]height^{2}[/tex], so that means one side of the square is: [tex]\sqrt{A}[/tex].
If then we have to bend the wire to form a equilateral triangule, all the sides must be equal, so one side of the triangule is [tex][tex]\sqrt{A} *\frac{4}{3}[/tex][/tex]. We have to multiply [tex]\sqrt{A} *4[/tex] in this case to obtain the total lenght of the wire.
According to the formula of the equilateral triangule:
[tex]A=\frac{\sqrt{3} }{4} *s^{2}[/tex]
where S is one side, The area will be:
[tex]Area=\frac{\sqrt{3} }{4} *(\sqrt{A}*\frac{4}{3} )^{2}=0.77A[/tex]
