Area Of A Regular Octagon Math

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. A regular octagon has schläfli symbol 8 and can also be constructed as a quasiregular truncated square t 4 which alternates two types of edges a truncated octagon t 8 is a hexadecagon 16 a 3d analog of the octagon can be the rhombicuboctahedron with the. You will obtain the total area of the octagon.

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A regular octagon has.

Area of a regular octagon math. Area of octagon 8 times frac a 2 4 1 sqrt 2 area of an octagon 2a 2 1 sqrt 2 formula for perimeter of an octagon. Extending the 4 non adjacent sides of a regular octagon with side length s will create a square as shown by the dashed blue lines above. A regular octagon can be thought of as being composed of 4 kite shaped areas. This is fairly easy to prove if it isn t a formula you already know.

Since there are as many of these triangles as the polygon has sides eight for an octagon you have to multiply the area of this triangle by the number of sides. The area of a regular octagon with side length s is. 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 2 1 2 s2 or approximately 4 828427 s2 where s side length width w 1 2 s.

Area of the octagon 8 x area of triangle. So perimeter will be the sum of the length of all sides. Area of a regular octagon. You will learn both the technique and then the formula.

Calculate the area of a regular octagon if each side is 5 cm and the width across the flats is 12 cm. Exterior angles of 45. 120 cm 5 cm 12 cm. 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.

Area of a regular octagon. Perimeter of an octagon is defined as the length of the boundary of the octagon. Interior angles of 135. It also forms four 45 45 90 right triangles on the four corners of the square.

In this video you will learn how to find the area of a regular octagon given the side length. In geometry an octagon from the greek ὀκτάγωνον oktágōnon eight angles is an eight sided polygon or 8 gon. The hypotenuse of the right triangles are s. From there you can determine the area of the large square by squaring it.

The area of a kite with diagonals d and w is xxxareakite d w 2. If you label a as the length of one side of an octagon then the sides of the large square are. Area of octagon 8 base height 2 perimeter apothem 2. Note that the base of the triangle is the length of a side of the octagon.

One can think of the regular octagon as a square with corners that have been cut off or shortened.