how to find the area of irregular shape? step by step explain octogon?
Answers
Answer:
make it regular make it -1 =7
Answer:
If you want to know how to find the area of a regular octagon by hand, the easiest procedure is to apply the standard formula for the area of a regular polygon. The formula is the following:
area of regular polygon = perimeter * apothem / 2,
where the apothem is the distance for the center of the polygon to the mid-point of a side. The perimeter can be calculated a few ways: by summing up the length of each side, multiplying the length of one side by the number of sides, or, if you're feeling lazy, you can also use our perimeter of a polygon calculator.
A trick to remember this formula is to understand where it comes from. If you look at the apothem you can see that it's the height of a triangle made by taking a line from the vertices of the polygon/octagon to the center of it. The resulting triangle is what is called an isosceles triangle and its area is:
area of triangle = base * height / 2
as we explained in the triangle area calculator. Note that the base of the triangle is the length of a side of the octagon. 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. You will obtain the total area of the octagon:
area of octagon = 8 * base * height / 2 = perimeter * apothem / 2.
These tricks work for any polygon, e.g., hexagons and any other polygon you can think of, as long as it is regular. Apart from using triangles, there are other tricks you can use to calculate the area of an octagon if you don't remember the formula, but they will not work for other polygons. For example, if you imagine an octagon shape inside of a square you can see that the difference is only four right triangles. "How to find the area of a regular octagon with this information?" you might ask. Well, it is very easy:
Step-by-step explanation:
Calculate the area of the square (the side is 2*apothem),
Calculate the sides of the right triangles either by using the 45 45 90 triangle calculator or the fact that they are right isosceles triangles, and use the special right triangles calculator.
Subtract the area of a right triangle four times from the area of the square,
Enjoy success!
Alternatively, you can use this trick. If you organize the right triangles correctly, you can construct a square from all four of them. In this case, the hypotenuse is also the side of the octagon. Then you can calculate the area of the parallelogram you just made from the four right triangles, and subtract it from the area of the big square.