0
The interior angles of an octagon are 135 degrees, which means that if you extend one of the sides, the complementary external angle is 45 degrees. So imagine an octagon instead as a square with four cut out right triangles on the corners.
Let's start with the length of a side x. Since the right triangles have a hypotenuse x, we know that the legs are length (sqrt(2)/2)x. The area of the triangle is 1/2 * base * height, which means one triangle is x2 / 4. Since there are 4 triangles, the total area of the triangles is x2.
Next, we need the area of the square. One side is a leg of the octagon plus two legs of our triangles, which would be x + (sqrt(2)/2)x + (sqrt(2)/2)x = x + sqrt(2)*x. Square this, and you get 3x2 + 2*sqrt(2)*x2. But! Subtract the area of the triangles from this, and you get (after some redistributing):
A = 2x2 * (1 + sqrt(2))
Wiki User
∙ 11y ago
Add your answer:
Earn +20 pts
How do you find the area of an octagon?
The formula for the area of a regular octagon is:A = 2 (1+ SQRT(2)) s**2 , orA = 4.8284 s**2where A= the area of the octagon, ands is the length of one side s**2 indicates s squared or s times s
How do you find the square feet in an octagon?
Assuming it's an octagon with equal sides (s = length of one side in feet) the formula is approximately: Area = 4.8284*(s2)
What is the surface area of an octagon?
First of all, you did not provide measurements for the octagon. Second, surface area is meant for three-dimensional figures. Octagons are two-dimensional.
Is the area of a square or octagon larger?
The answer depends on their sizes! A small square will have a smaller area but a huge square will have a bigger area. Do the two shapes have equal sides, apothems, diagonals? Also, a square is a regular shape, what about the octagon?
What is the area for an octagon with a fixed perimeter of 300?
Approximately 6,789.98 units2
Which figure's area formula is most similar to the area formula for a parallelogram?
Octagon
What is the formula of octagon based pyramid?
Area = ( 2 + 2√2 )a2
What is the square footage of an octagon house that has 12 feet sides?
The formula for the area of an octagon is Area = (2 + 2√2)a2, where a is the length of each side. Area = (2 + 2√2)12ft2 = 695ft2
What is the formula for an octagon?
There is no formula for an octagon. There are formulas for figuring out different aspects of an octagon, such as its perimeter, diameter, etc.
How do you find the area of an octagon?
The formula for the area of a regular octagon is:A = 2 (1+ SQRT(2)) s**2 , orA = 4.8284 s**2where A= the area of the octagon, ands is the length of one side s**2 indicates s squared or s times s
How does the formula of a octagon work?
There is insufficient information for us to answer this question. Please edit the question to include more context or relevant information. What formula of an octagon are you referring to: the sum of the interior angles, the frustum of a regular octagon, the area, the perimeter, the number of diagonals? The possibilities are almost endless!
What is the formula to find the area of an octagon?
one way to do it is to first draw a rectangle around the octagon then multiply length by width then subtract the area of the four triangles out side the octagon from your total answer. OR You can use the formula A= 2 s2 cot(π/h) π is supposed to be pi s2 is supposed to be s squared Cot is an abbreviation for cotangent
What is the formula find the area of an octagon?
one way to do it is to first draw a rectangle around the octagon then multiply length by width then subtract the area of the four triangles out side the octagon from your total answer. OR You can use the formula A= 2 s2 cot(π/h) π is supposed to be pi s2 is supposed to be s squared Cot is an abbreviation for cotangent
How do you find the square feet in an octagon?
Assuming it's an octagon with equal sides (s = length of one side in feet) the formula is approximately: Area = 4.8284*(s2)
What is the formula for finding the area of a regular octagon?
A= 2(1 + sqrt2)S² where S is a side length
What is the formula to find the volume of an octagon?
You don't find the "volume" of a flat figure. Perhaps you want its surface area.The area for a regular octagon of side "a" is 2 (1 + root(2)) a2, where "root" isthe square root function. If it is not a regular octagon, I don't think there is asimple formula to find the area - you'll have to split it up into simpler figures,for example triangles.==================================Answer #2:Here is the formula, to which the first answer alluded in passing,but which, for some reason, it did not explicitly present:Volume of an Octagon = 0 .
A regular octagon with sides of length 7 and an apothem of length 8.45 has an area of how many 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, (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.)
