But in the case of the irregular octagon, the sides have different dimensions and each angle could be different. Thus in my diagram each of the pink trapezoids has area $\large \frac{42 + 30}{2} \normalsize \times d$ … B = 7m The area of an octagon = 2 x (1 + √2) x B2 Area = 2 x (1 + 1.414213562) x 72 Thus to complete the area calculation you need to know the distance $d.$. Otherwise it is an irregular octagon. Let us understand the above steps with the help of an example. It could also be either convex or concave. The area of a trapezoid is the average of the lengths of the parallel sides times the distance between the parallel sides. Find the area of an irregular octagon given below: The given figure is an irregular octagon. One technique is to subdivide the octagon into six triangles as in the diagram. If all interior angles of an octagon or polygon are less than 180°, it is convex. 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Octagons and other polygons can also be classified as either convex or concave. Octagon has 8 sides and 8 angles. The distance of each vertex from the centre is equal. The area of an octagon formula is given as. Otherwise, the polygon is known as an irregular polygon. In Geometry, we have studied different types of polygon shapes such as triangle, square, pentagon, hexagon, rectangle, etc. It may be possible to find the area of your octagon with fewer calculations but without seeing the actual shape of the octagon the technique above is the best I can do. The area of a trapezoid is the average of the lengths of the parallel sides times the distance between the parallel sides. Irregular polygons are not considered as having a centre and are not symmetric. 1. Note that the base of the triangle is the length of a side of the octagon. Area of a regular octagon, A = 2a2 (1+√ 2 ) Square units. Hence, the area of an irregular octagon is 108.83 square units Visit BYJU’S – The Learning App to learn more Maths-related concepts and download the app to watch interesting videos. A regular octagon has all its sides equal in length. If you can measure the sides of the six triangles then you can find their areas using Heron's formula. An irregular octagon is one which has 8 different sides. Hence, here we are providing some important steps to find the area of an irregular octagon. The measurement unit for the area is square units. Like other shapes, the octagon is also a polygon. They are not curved or disjoint with each other. Where “a” is the length of the octagon sides. Thus in my diagram each of the pink trapezoids has area $\large \frac{42 + 30}{2} \normalsize \times d$ square units. In the above figure, you can see the figure of a regular octagon, which is divided into eight equivalent triangles. Measurements are 4 equal sides of =BD", and 4 equal sides of =BE". It measures 1 1/2" = from flat to flat. If so then the octagon can be partitioned into there pieces, a rectangle, which is 42 units by 21 units and hence has an area of $42 \times 21$ square units, and two congruent trapezoids. Area of an Irregular Polygon Unlike a regular polygon, unless you know the coordinates of the vertices, there is no easy formula for the area of an irregular polygon. Visit BYJU’S – The Learning App to learn more Maths-related concepts and download the app to watch interesting videos. Therefore, the area of an irregular octagon ABCDEFGH is given below: Area of ABCDEFGH = Area of ABC + Area of ACD + Area of ADE +Area of ADE + Area of AFG + Area of AGH, Therefore, the area of ABC = \(\sqrt{S(S-a)(S-b)(S-c)}\) Area of a regular octagon, A = 2a2 (1+√ 2 ) Square units. The length of rectangle is 42 and the width is 21 and and the base length is 42-12 =30 i mean the Finding the area of a regular octagon is an easy task because you have been provided by a symmetric figure. In a regular polygon, there are 8 sides of equal length and equal internal angles – 1350. So, to find its area, it is divided into other regular polygons. 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 the octagon is the sum of the areas of the six triangles. if i have a rectangular octagon then how i can find its area 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 can prove that to yourself if you feel like it). Similarly, we can find the area of other triangles using Heron’s formula, Area of ABCDEFGH = 7.64 + 11.83 + 14.14 + 11.