If the perimeter is 48 inches then each side is 8 inches.
The angle at the centre that subtends to adjacent vertices is 360/6 = 60degrees.
Therefore the hexagon consists of 6 equilateral triangles of sidelength 8 units.
Using Heron's formula
$$\\Area = 6 \;\; *\;\; \sqrt{s(s-a)(s-b)(s-c)}\qquad where\quad s=(a+b+c)/2\\\\
s=24/2=12\\\\
Area = 6 \;\; * \;\; \sqrt{12(12-8)(12-8)(12-8)}\\\\
Area = 6 \;\; * \;\; \sqrt{12*64}\\\\
Area = 6 \;\; * \;\; 8\sqrt{4*3}\\\\
Area = 6 \;\; * \;\; 16\sqrt{3}\\\\
Area = 96\sqrt{3}\;\;inches^2\\\\$$
If the perimeter is 48 inches then each side is 8 inches.
The angle at the centre that subtends to adjacent vertices is 360/6 = 60degrees.
Therefore the hexagon consists of 6 equilateral triangles of sidelength 8 units.
Using Heron's formula
$$\\Area = 6 \;\; *\;\; \sqrt{s(s-a)(s-b)(s-c)}\qquad where\quad s=(a+b+c)/2\\\\
s=24/2=12\\\\
Area = 6 \;\; * \;\; \sqrt{12(12-8)(12-8)(12-8)}\\\\
Area = 6 \;\; * \;\; \sqrt{12*64}\\\\
Area = 6 \;\; * \;\; 8\sqrt{4*3}\\\\
Area = 6 \;\; * \;\; 16\sqrt{3}\\\\
Area = 96\sqrt{3}\;\;inches^2\\\\$$