You can only do this for a regular octagon.
It is much easier to understand the method if you do a rough sketch and follow the explanation using that. Unfortunately, this browser does not support any kind of drawing!
Suppose the diameter of the octagon is D. Therefore the diameter of the circumscribing circle is also D.
Form the centre of this circle, draw lines to two adjacent vertices of the octagon. The lengths of these lines is D/2 because these are radii of the circle. These lines and the side of the octagon form an isosceles triangle, and the apothem is the height of this triangle.
Now consider half this triangle: the right angled triangle formed by the apothem, half the side of the octagon and the radius.
The angles at the apex of the octagon is 360/8 = 45 degrees. So the angle at the apex of the right angled triangle is half that = 22.5 degrees.
Then cos(22.5 deg) = Apothem/Radius
So that Apothem = Radius*cos(22.5 deg) = D/2*0.9239 (approx).
an octagon doesn't have a volume its has and area ecause it is a 2-d figure. to find the area of a 2-d regular figure it is 1/2 apothem * perimeter (apothem is the distance of a line from the center of a polygon, to the midpoint of a side)
130 to find the area of any regular polygon, multiply the perimeter by one-half the apothem. This is the same as multiplying the side-lengths by the number of sides by one-half the apothem.
Area in square units = 0.5*(apothem)*(perimeter)
An octagon with a side length of 5.8 cm has an apothem that is approximately 7 cm. The area of such a shape is approx 162.4 sq cm.
i think its 10
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an octagon doesn't have a volume its has and area ecause it is a 2-d figure. to find the area of a 2-d regular figure it is 1/2 apothem * perimeter (apothem is the distance of a line from the center of a polygon, to the midpoint of a side)
About 289
130 to find the area of any regular polygon, multiply the perimeter by one-half the apothem. This is the same as multiplying the side-lengths by the number of sides by one-half the apothem.
By joining all the vertices to the centre of the octagon, the apothem forms the height of the triangles with the side of the regular octagon as the base. This the area is 8 × area_triangles = 8 × ½ × side × apothem = 4 × side × apothem: Area_regular_octagon = 4 × side_length × apothem ≈ 4 × 4 in × 4.8 in = 76.8 in²
There is nothing in the question to indicate that it is a regular octagon and since that cannot be assumed, there is not enough information to calculate its area. Even if it were regular, the answer will depend what the 8-foot measure refers to: the length of a side of the octagon, its diameter, its apothem etc.
Area in square units = 0.5*(apothem)*(perimeter)
8.31 ft (approx).8.31 ft (approx).8.31 ft (approx).8.31 ft (approx).
An apothem of a regular polygon is a segment from its center to the midpoint of a side. You can use the apothem to find the area of a regular polygon using this formula: A = pa/2 where p is the perimeter of the figure and a is the apothem. For a regular octagon with side length 11, the perimeter p = 8(11) = 88. So the area would be A = 88(8.85)/2 = 389.4 square units.
The area of a regular octagon: A = (2 x apothem)2- (length of side)2 or in this case A= (2 x 8.45)2 - 72
An octagon with a side length of 5.8 cm has an apothem that is approximately 7 cm. The area of such a shape is approx 162.4 sq cm.
By Apothem LengthThe area of a regular octagon can also be computed using its measured apothem (a line from the center to the middle of any side). The formula for an octagon with side length s and apothem a is Area = a4s . (apothem times one-half the perimeter)So for this example, (8 cm and 9.66 cm) Area = (9.66)(32) = 309.12 cm2----By Side LengthThe area of a regular octagon with side length s is given as Area = 4.828427 s2 , so for a regular octagon of side length 8 cm , the area is calculated as 309.02 cm2. (indicating an error from rounding the apothem length)(This formula is generated by adding or subtracting the missing corner triangles.)