A3. A square, a circle, and an equilateral triangle have the same perimeter of $36 \mathrm{~cm}$. Which of these shapes has the largest area?
(A) triangle
(B) $\mathrm{circle}$
(C) square
(D) All shapes have the same area.
(E) It is not possible to determine.
A3. The side length of the square is $a=\frac{36}{4}=9 \mathrm{~cm}$, and the area of the square is $81 \mathrm{~cm}^{2}$. The equilateral triangle has a side length of $a=\frac{36}{3}=12 \mathrm{~cm}$ and an area of $\frac{144 \cdot \sqrt{3}}{4} \doteq 62.4 \mathrm{~cm}^{2}$. The radius of the circle is $r=\frac{36}{2 \pi}$, and the area of the circle is $\frac{\pi \cdot 36^{2}}{2^{2} \cdot \pi^{2}} \doteq 103.2 \mathrm{~cm}^{2}$. The circle has the largest area.