o find the area of a square given the length of one of its diagonals, we can use the relationship between the side length of the square and its diagonal.

The diagonal $dd$d of a square with side length $ss$s can be found using the Pythagorean theorem in the context of the square’s right triangle formed by two sides and the diagonal:

$d=s\sqrt{2}d\; =\; s\backslash sqrt\{2\}$d=s2​Given that the diagonal $dd$d is 3.8 meters, we can solve for the side length $ss$s:

$3.8=s\sqrt{2}3.8\; =\; s\backslash sqrt\{2\}$3.8=s2​Solving for $ss$s, we get:

$s=\frac{3.8}{\sqrt{2}}=\frac{3.8}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{3.8\sqrt{2}}{2}=\frac{3.8\times 1.414}{2}=\frac{5.3732}{2}=2.6866 meterss\; =\; \backslash frac\{3.8\}\{\backslash sqrt\{2\}\}\; =\; \backslash frac\{3.8\}\{\backslash sqrt\{2\}\}\; \backslash cdot\; \backslash frac\{\backslash sqrt\{2\}\}\{\backslash sqrt\{2\}\}\; =\; \backslash frac\{3.8\backslash sqrt\{2\}\}\{2\}\; =\; \backslash frac\{3.8\; \backslash times\; 1.414\}\{2\}\; =\; \backslash frac\{5.3732\}\{2\}\; =\; 2.6866\; \backslash text\{\; meters\}$s=2​3.8​=2​3.8​⋅2​2​​=23.82​​=23.8×1.414​=25.3732​=2.6866 metersNow, to find the area $AA$A of the square, we use the formula for the area of a square:

$A=s^{2}A\; =\; s^2$A=s2Substituting the value of $ss$s:

$A=(2.6866{)}^2=7.2151 square metersA\; =\; (2.6866)^2\; =\; 7.2151\; \backslash text\{\; square\; meters\}$A=(2.6866)2=7.2151 square metersThus, the area of the square is approximately $7.227.22$7.22 square meters.