Question

A wire is bent to form an equilateral triangle. If the area of the triangle is 4 3 cm, what is the area of the circle formed (in cm) by the same wire?​

Answer 1

Answer:

The area of an equilateral triangle formed by bending a metal wire is 484

3

sq.cm

Let the side of equilateral triangle be xcm

We know that

Area of equilateral triangle=

4

3

×x

2

⇒484

3

=

4

3

×x

2

⇒x

2

=484×2

⇒x=

484×2

=44

∴ the side of equilateral triangle is 44cm

Perimeter of equilateral triangle=3×side=3×44=132cm

So, the perimeter of equilateral triangle is 132cm

So, the perimeter of equilateral triangle is 132cm

Perimeter of equilateral triangle is nothing but total lenght of the wire .

Hence the total length of the wire is =132 cm

If the circle is formed its circumference is 132 cm

We know that circumference of circle=2πr

Area of the circle=πr

2

=

7

22

×21×21=22×3×21=1386sq.cm