A uniform conducting wire of length 12a and resistance R is wound...

Area of equilateral triangle of side a,

$A = \dfrac{1}{2} \times a \times \dfrac{\sqrt{3}a}{2} = \dfrac{\sqrt{3}}{4}{a}^{2}$

Magnetic moment of each triangle,

$m = IA = \dfrac{\sqrt{3}}{4}{a}^{2}I$

$12a$ length of wire will form $4$ loops of triangle of side $a$.

Magnetic moment of triangle,

${M}_{1} = Nm = 4 \times \dfrac{\sqrt{3}}{4}{a}^{2}I = \sqrt{3}I{a}^{2}$

Similarly, magnetic moment of square

${M}_{2} = Nm = 3 \times \left(I{a}^{2}\right)$

$= 3I{a}^{2}$