It is 9.1 inches (approx).
L*[sin(x) + sin(2x) + sin(3x) +sin(4x)] = 28 inches where x = 360/10 = 36 degrees.
Since x = 36 deg,
sin(x) = sin(4x) and sin(2x) = sin(3x)
So
L*[2sin(x) + 2sin(2x)] = 28 inches
L*[sin(x) + sin(2x)] = 14 inches
L* 1.539 = 14 approx so that L = 9.098 inches or 9.1 inches, approx.
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A decagon is a 10-sided figure. If each side is 9.9 feet long, the perimeter of the decagon, which is the sum of all sides, is 10 x 9.9 feet or 99 feet.
A decagon is a shape that has ten sides. As long as the figure has ten sides to it, then it is a decagon.
Each side of the 48 inch perimeter is 6 inches long, therefore there are 48 / 6 = 8 of them. The figure is a regular octagon.
There is insufficient information to answer the question. There is no indication that the octagon is regular and therefore, you may not assume that it is. Even it you were told that it is a regular octagon, there is still insufficient information: the answer will depend on what the 17.25 inch is a measure of - the diagonal of the octagon or its height (width).
If you can draw a line 1 inch long and divide it into 8 equal parts, then each of the segments would be an eighth of an inch long