Calculate area, perimeter, diagonals, apothem, and circumradius of a regular octagon
Area:
A = 2(1 + √2) × s²
Perimeter:
P = 8 × s
Short Diagonal:
d₁ = s × √(2 + √2)
Long Diagonal:
d₂ = s × (1 + √2)
Apothem:
a = (s / 2) × (1 + √2)
Circumradius:
R = s × √(4 + 2√2) / 2
A regular octagon is an eight-sided polygon where all sides have equal length and all interior angles are equal (135 degrees each). It has 8 lines of symmetry and rotational symmetry of order 8.
The area of a regular octagon is calculated using the formula A = 2(1 + √2) × s², where s is the side length. This formula comes from dividing the octagon into triangles and calculating their combined area.
A regular octagon has two types of diagonals. Short diagonals connect vertices separated by two sides, while long diagonals connect vertices separated by three sides. The long diagonal is always longer than the short diagonal.
Octagons are commonly seen in stop signs, architectural designs, gazebos, and decorative patterns. They are popular in design because they combine the stability of squares with the aesthetic appeal of circles.
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