A regular octagon has eight straight sides of equal length, where each side touches another side and thus is a "closed" shape. All interior angles are 135 degrees, and all exterior angles are 45 degrees. If you know the length of one of the sides, the area inside a regular octagon is simple to find using a standard formula: 2 a^2 (1 + sqrt2), where "a" is the length of one of the sides.
For example, find the area of an octagon with sides 3 inches long, or a = 3. Find the square of a, which means multiplying a by itself: 3^2 = 3 3 = 9. Next, multiply the square of a by 2: 2 9 = 18. Calculate the value of (1 + sqrt2); the square root of 2 is roughly 1.414, so 1 + 1.414 = 2.414. Multiply both numbers: 18 * 2.414. This gives a final answer of roughly 43.45 inches.
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