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(C) The perimeter of each shape is $P = 132 \, cm$.$1$. For an equilateral triangle: $3a = 132 \implies a = 44 \, cm$. Area $= \frac{\sqrt{3}}{4} a^2

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Circle

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(C) The perimeter of each shape is $P = 132 \, cm$.$1$. For an equilateral triangle: $3a = 132 \implies a = 44 \, cm$. Area $= \frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} 	imes 44^2 \approx 0.433 	imes 1936 \approx 838.31 \, cm^2$.$2$. For a square: $4a = 132 \implies a = 33 \, cm$. Area $= a^2 = 33^2 = 1089 \, cm^2$.$3$. For a regular hexagon: $6a = 132 \implies a = 22 \, cm$. Area $= \frac{3\sqrt{3}}{2} a^2 = \frac{3\sqrt{3}}{2} 	imes 22^2 \approx 2.598 	imes 484 \approx 1257.47 \, cm^2$.$4$. For a circle: $2\pi r = 132 \implies r = \frac{132}{2 	imes (22/7)} = 21 \, cm$. Area $= \pi r^2 = \frac{22}{7} 	imes 21^2 = 1386 \, cm^2$.Comparing the areas: $838.31 < 1089 < 1257.47 < 1386$. Thus,the circle has the largest surface area.

$A$ piece of wire $132 \, cm$ long is bent successively in the shapes of an equilateral triangle,a square,a regular hexagon,and a circle. Then,which has the largest surface area?

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