Question

A copper wire when bent in the form of an equilateral triangle has an area of 121√3 cm^2
the same wire is bent into the form of a circle, find the area enclosed by the wire.​

Answer 1

Answer:

A copper wire is bent in the form of an equilateral triangle and has area 121√3 centimetre squared. . If the same wire is bent into the form of a circle. What is the area enclosed by wire?

Here, The area of an equilateral triangle=121√3 cm²

So, Each side of the equilateral triangle=√[(4×Area)/√3]

=√[(4×121√3)/√3]

=√(4×121)

=2×11

=22 cm.

Since, This equilateral triangle is formed by bending a copper wire.

So, the length of copper wire=perimeter of the equilateral triangle

=3×side

=3×22

=66 cm

Now, the copper wire is bent into the form of a circle.

Then the circumference of the circle (c)=66cm

So ,the radius (r)=c/2π

=66/(2×22/7)

=(66×7)/(2×22)

=21/2 cm.

Hence, the area of the circle=πr²

=(22/7)×(21/2)²

=(22/7)×(441/4)

=(11×63)/2

=693/2

=346•5 cm²,Ans.

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