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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).
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∙ 9y ago
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The formula for volume of an octagon?
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)
What is the area of a regular octagon with a side of 6.5 and an apothem 5?
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.
A regular octagon with sides of length 7 and an apothem of length 10.49 has an area of?
Area in square units = 0.5*(apothem)*(perimeter)
What is the area of a regular octagon with a side length of 5.8 centimeters and an apothem length of 7 centimeters?
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.
If a regular octagon's apothem is 14.5cm and the length of the side is 12cm what is the area?
i think its 10
Find the area of a regular octagon with apothem K and side of 10?
40K
What is the area of a regular octagon with an apothem of 8.5?
About 289
The formula for volume of an octagon?
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)
What is the area of a regular octagon with a side of 6.5 and an apothem 5?
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.
What is the area of a regular octagon with a side length of 4 inches and an apothem length of 4.8 inches?
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
How many square feet in a 8 foot octagon?
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.
A regular octagon with sides of length 7 and an apothem of length 10.49 has an area of?
Area in square units = 0.5*(apothem)*(perimeter)
What is the apothem of a regular octagon with a diameter of 18 feet?
8.31 ft (approx).8.31 ft (approx).8.31 ft (approx).8.31 ft (approx).
A regular octagon with sides of length 11 and an apothem of length 8.85 has an area of what?
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.
A regular octagon with sides of length 7 and an apothem of length 8.45 has an area of what?
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
What is the area of a regular octagon with a side length of 5.8 centimeters and a apothem of 7 centimeters?
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.
What is the area of a regular octagon with a side length of 5.8 centimeters and an apothem length of 7 centimeters?
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.
