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

$\frac{ \sqrt{3} }{4} \times {a}^{2} = 4 \sqrt{3} \\ {a}^{2} = 4 \sqrt{3} \times \frac{4}{ \sqrt{3} } \\ {a}^{2} = 16 \\ a = 4 \\ perimeter \: of \: square \: = perimeter \: of \: circle \\ 4a = 2\pi {r}^{2} \\ 4 \times 4 =2 \times \frac{22}{7} \times r \\ 16 \times \frac{7}{22} \times \frac{1}{2} = r \\ r = 2.5 \\ area \: of \: circle = \pi {r}^{2} \\ = \frac{22}{7} \times {2.5}^{2} \\ = 19.6 {cm}^{2}$