Area Of Regular Octagon Math

The area of a regular octagon with side length s is.

Area of regular octagon math. S 2a 2 1 sqrt 2 i tried to prove this by the area of 8 isoscles triangles inside the octagon but i didn t manage to find the area of those triangles. What is the area of the regular octagon below. You can calculate the area of a regular octagon with the standard regular polygon method but there s a nifty alternative method based on the fact that a regular octagon is a square with its four corners cut off. If you label a as the length of one side of an octagon then the sides of the large square are a sqrt 2 1.

120 cm 5 cm 12 cm. The area would be 309 02. In order to calculate the area of an octagon we divide it into small eight isosceles triangles. It also forms four 45 45 90 right triangles on the four corners of the square.

A regular octagon has. Area 2 1 2 s2 or approximately 4 828427 s2 where s side length width w 1 2 s. The hypotenuse of the right triangles are s. For example here s how you d find the area of eightplu in the figure below given that it s a regular octagon with sides of length 6.

Ask question mathematics. Area of an octagon is defined as the region occupied inside the boundary of an octagon. The four corners like triangle sue in the figure that you cut off the square to turn it into an octagon are 45 45 90 triangles you. Area of a regular octagon.

Determine the area of a regular octagon with vertices on the unit circle closed 2 answers closed 3 years ago. Calculate the area of a regular octagon if each side is 5 cm and the width across the flats is 12 cm. Calculate the area of one of the triangles and then we can multiply by 8 to find the total area of the polygon. One can think of the regular octagon as a square with corners that have been cut off or shortened.

Exterior angles of 45. From there you can determine the area of the large square by squaring it a 2 3 2 sqrt 2. Area of a regular octagon. Prove that the area of an octagon with side a can be computed by the formula.