2012 CEMC Gauss (Grade 7) Problems/Problem 11

Problem

The perimeter of a square is $36$ cm. The area of the square, in $cm^{2}$ , is

$\text{ (A) }\ 24 \qquad\text{ (B) }\ 81 \qquad\text{ (C) }\ 36 \qquad\text{ (D) }\ 1296 \qquad\text{ (E) }\ 324$

All of the side lengths of a square are equal, and there are four sides in a square. This means that we can let $s$ be the side length of the square.

Setting up an equation, we get:

$4s = 36$

$s = 9$ cm

The area of a square is the square of its side length, giving:

$s^{2} = (9 cm)^{2} = 81 cm^{2}$

Thus, the answer is $\boxed {\textbf {(B) } 81}$ .