If the gym is a square with 17 meters sides, its area is given (as any other square) by the square of the side:
[tex] A_{gym} = 17^2 = 289 \text{ m}^2[/tex]
So, the area of the classroom is
[tex] A_{class} = \dfrac{289}{2}=144.5 \text{ m}^2[/tex]
We can deduce the side of the classroom only assuming that it is a square as well: if this is the case, the side of a square with given area is the square root of the area, so we have
[tex] s_{class} = \sqrt{144.5} \approx 12.02 \text{ m} [/tex]
