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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.
An apothem is a line segment from the center of a regular polygon to the midpoint of a side.
Each exterior angle of a regular octagon is 360/8 = 45 degrees
Radii are related to circles.What do you mean by an "...octagon with a radius..."?Unless the octagon is regular it is impossible to to calculate the area of the octagon from one measurement alone.So assuming that the octagon is a regular octagon, what do you mean by radius? Do you mean:the radius of the circumcircle which passes through all verticesarea regular octagon = 8 × ½ × 8 × 8 × sin(360°/8) units² = 256 × sin(45) units²= 256 × 1/√2 units²= 128√2 units²≈ 181 units²the radius of the inscribed circle, which is the apothem of the octagonarea regular octagon = 8 × 8 × 8 × tan((360°/8)/2) units² ≈ 196 units²Something elseRe-ask your question explaining what you mean by "radius".
About 289
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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
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
Area in square units = 0.5*(apothem)*(perimeter)
309.12
i think its 10
463 square units
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.)
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.
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 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, (7 cm and 8.45 cm) Area = (8.45)(28) = 236.6 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 7 cm , the area is also about 236.6 cm2.(This formula is generated by adding or subtracting the missing corner triangles.)