An octagon with a perimeter of 96 m with sides 96/8=12m. The area of an octagon with 12m sides is 695.29m. Do you need equation?
The smoothed octagon is a geometrical construction conjectured to have the lowest maximum packing density of the plane of all centrally symmetric convex shapes. It is constructed by replacing the corners of a regular octagon with a section of a hyperbola that is tangent to the two sides adjacent to the corner and asymptotic to the sides adjacent to these.
The smoothed octagon has a maximum packing density, ηso given by
Octagon houses were a unique house style briefly popular in the 1850s in the United States and Canada. They are characterised by an octagonal (eight-sided) plan, and often feature a flat roof and a veranda all round. Their unusual shape and appearance, quite different from the ornate pitched-roof houses typical of the period, can generally be traced to the influence of one man, amateur architect and lifestyle pundit Orson Squire Fowler. Although there are other octagonal houses worldwide, the term octagon house usually refers specifically to octagonal houses built in North America during this period, and up to the early 1900s.