To solve this problem, let us first calculate for the Perimeter of the other octagon. The formula for Perimeter is:
Perimeter = n * l
Where n is the number of sides (8) and l is the length of one side. Let us say that first octagon is 1 and the second octagon is 2 so that:
Perimeter 2 = 8 * 16.35 in = 130.8 inch
We know that Area is directly proportional to the square of Perimeter for a regular polygon:
Area = k * Perimeter^2
Where k is the constant of proportionality. Therefore we can equate 1 and 2 since k is constant:
Area 1 / Perimeter 1^2 = Area 2 / Perimeter 2^2
Substituting the known values:
392.4 inches^2 / (87.2 inch)^2 = Area 2 / (130.8 inch)^2
Area 2 = 882.9 inches^2
Therefore the area of the larger octagon is about 882.9 square inches.
