Answer: Yes.
The perimeter is about 42.86 m Round to 42.9 m
The area is about 138.59 m² . Round to 138.6 m²
Explanation:
To find the perimeter, you need the length of the sides. Imagine the octagon as 8 isosceles triangles assembled. You need the length of the short (exterior) side to calculate the perimeter.
With only the length of the ray given, you could use some trig. A calculator is necessary!
The octagon has 8 sides, you can calculate the size of the central angle between two radii 360/8 = 45. Subtract from 180 and divide by 2 to get the measure of one of the equal angles.
That angle measure is 67.5° Use cos(67.5)(7) = 2.678784027 the length of half of the side-- between the dotted line and the ray in the diagram.
2(2.678784027)(8) = 42.86054443 is the perimeter.
The area of each isosceles triangle is bh/2.
Find the height by using sin(67.5)(7) = 6.467156728
The cos(67.5)(7) is already half the base. Use as is!
6.467156728 × 2.678784027 = 17.32411614
This is the area of 1 of the 8 imaginary triangles, so multiply by 8 for the whole area of the octagon.
17.32411614 × 8 = 138.5929291
I hope this helps. Complicated!
There may be easier ways, but this is the only way I know at this point.