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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))
What else can I help you with?
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.
What is the formula for calculating the volume of an octagonal prism?
Calculating the volume (V) of an octagonal prism involves finding the area (A) of the octagon that is an end (or base), and then simply multiplying it by the length (L) of the prism. The area of an octagon with a side of length s is given by this formula: Aoctagon = 2 (1 + sqrt 2) s2 or about 4.8284 s2 If we take that and multiply it by the length of the prism, we should arrive at the volume thus: Voctagonal prism = L x Aoctagon
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 can you find the area of a shaded region assuming the octagon is regular?
To find the area of a shaded region within a regular octagon, first calculate the area of the entire octagon using the formula ( A = 2(1 + \sqrt{2})s^2 ), where ( s ) is the length of a side. Then, determine the area of any non-shaded regions (such as triangles or smaller shapes) within the octagon and calculate their total area. Finally, subtract the area of the non-shaded regions from the total area of the octagon to find the area of the shaded region.
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)
A regular octagon has an apothem measuring 10 in. and a perimeter of 66.3 in. What is the area of the octagon rounded to the nearest square inch?
To find the area of a regular octagon, you can use the formula: Area = (Perimeter × Apothem) / 2. Given the perimeter is 66.3 inches and the apothem is 10 inches, the area calculates to: Area = (66.3 × 10) / 2 = 331.5 square inches. Rounding to the nearest square inch, the area of the octagon is approximately 332 square inches.
