Q: What is the length of each side of an octagon that is 48 inches in diameter?

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8 sides each 9 inches: 6 feet

I presume by diameter of an octagon you mean the length of the diagonal between opposite vertices of a regular octagon. By completing all the diagonals between opposite vertices of a regular octagon, it divides it up into 8 equal isosceles triangles, with their apexes at the centre of the octagon. The two sides of these isosceles triangles which go from a vertex of the octagon to the centre has a length half that of the diameter. If the centre point of each side of the octagon is joined to the centre of the octagon, each of the 8 isosceles triangles above are split into two (congruent) right angled triangles. The angle at the centre of the octagon of each of these triangles is (360° ÷ 8) ÷ 2 = 22.5°. The side opposite this angle is half the length of the side of the octagon and so the perimeter is 16 times its length. The hypotenuse of the right angled triangles is half the diameter. Thus the trigonometric sine function can be used to find half the octagons side length, and thus its perimeter: sin = opp/hyp → opp = sin x hyp Perimeter = 16 x opp = 16 x (sin 22.5° x diameter/2) = diameter x 8 x sin 22.5° ≈ diameter x 3.061 This can be generalised to any regular even sided polygon if diameter is defined as the length of the diagonal between opposite vertices (which is also the maximum straight line distance between two points on the perimeter): perimeter = diameter x number_of_sides x sin(180° ÷ number_of_sides) As the number of sides increases, "number_of_sides x sin(180° ÷ number_of_sides)" gets closer and closer to π.

A plane shape is regular if each of its sides is of the same length AND each of its angles is of the same measure. An octagon can be regular or irregular.

The side length of a regular octagon whose principal diagonal is 25 feet is 9.57 feet, approx.

An octagon has eight sides, in this case all the same length. Total length of eight sides = 40 cm. Length of each side = 40 divided by 8 equals 5 cm

Related questions

An octagon is a polygon with 8 sides. To find the diameter of a regular octagon when each side is 18 inches in length, you can use the formula: Diameter = Side length × √(2 + √2) Plugging in the given side length (18 inches): Diameter = 18 × √(2 + √2) ≈ 56.97 inches So, the diameter of the octagon is approximately 56.97 inches.

Diameter = 88.84 inches

An octagon is an eight-sided figure. If a regular octagon has a perimeter of 24 inches, then each side will be 24 / 8 = 3 inches.

The length of a single edge of an octagon can be calculated by measuring the diameter, then dividing this length by the square root of the sum of four and two times the square root of two, which would be written in a calculator as sqrt(4+(2*sqrt(2))). In this case, a five inch diameter equates to approximately 1.913 inches per side.

8 sides each 9 inches: 6 feet

A regular octagon has 8 sides so if each side is 3 1/2 inches long then the perimeter is just 8*(3 1/2 inches) or 28 inches

Each of the 10 sides of the decagon is 1.9314 inches long.

I presume by diameter of an octagon you mean the length of the diagonal between opposite vertices of a regular octagon. By completing all the diagonals between opposite vertices of a regular octagon, it divides it up into 8 equal isosceles triangles, with their apexes at the centre of the octagon. The two sides of these isosceles triangles which go from a vertex of the octagon to the centre has a length half that of the diameter. If the centre point of each side of the octagon is joined to the centre of the octagon, each of the 8 isosceles triangles above are split into two (congruent) right angled triangles. The angle at the centre of the octagon of each of these triangles is (360° ÷ 8) ÷ 2 = 22.5°. The side opposite this angle is half the length of the side of the octagon and so the perimeter is 16 times its length. The hypotenuse of the right angled triangles is half the diameter. Thus the trigonometric sine function can be used to find half the octagons side length, and thus its perimeter: sin = opp/hyp → opp = sin x hyp Perimeter = 16 x opp = 16 x (sin 22.5° x diameter/2) = diameter x 8 x sin 22.5° ≈ diameter x 3.061 This can be generalised to any regular even sided polygon if diameter is defined as the length of the diagonal between opposite vertices (which is also the maximum straight line distance between two points on the perimeter): perimeter = diameter x number_of_sides x sin(180° ÷ number_of_sides) As the number of sides increases, "number_of_sides x sin(180° ÷ number_of_sides)" gets closer and closer to π.

An octagon that is not irregular is a regular octagon, one in which each of the eight sides os the same length

168.8 cubic inches

Any length greater than zero.

A plane shape is regular if each of its sides is of the same length AND each of its angles is of the same measure. An octagon can be regular or irregular.