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
A side of 4 inches does not correspond exactly to an apothem of 4.8 inches.
Side of a regular octagon = 4 inches =>apothem is 4.83 inches, approx
and area = 77.3 sq inches.
Or
Apothem = 4.8 inches =>
side = 3.98 inches, approx
and area = 76.3 sq inches.
232.57 square inches.
We know that the height of an equilateral triangle equals the product of one half of the side length measure with square root of 3.Since in our regular hexagon we form 6 equilateral triangles with sides length of 16 inches, the apothem length equals to 8√3 inches.
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.
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112 inches, that is if all the sides are the same length .I think.
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
309.12
Area in square units = 0.5*(apothem)*(perimeter)
309.12
389.40
293.72
i think its 10
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 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.
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, (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.)
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.