20.94 A circle and a square have equal perimeters, then
(A) their areas are equal.
(B) the area of the circle is larger.
(C) the area of the square is larger.
(D) the area of the circle is $\pi$ times the area of the square.
(E) other.
(3rd American High School Mathematics Examination, 1952)
[Solution] Let the radius of the circle with perimeter $p$ be $r$, and the side length of the square be $a$. Thus, $r=\frac{p}{2 \pi}, a=\frac{p}{4}$.
$$
S_{\odot}=\pi r^{2}=\frac{p^{2}}{4 \pi}, \quad S_{\square}=\left(\frac{p}{4}\right)^{2}=\frac{p^{2}}{16},
$$

Clearly, $4 \pi S_{\square}$.
Therefore, the answer is $(B)$.