It depends on the nature of the polygon and what information is available. There are relatively simple formulae for regular polygons. Some shapes can be decomposed into smaller shapes whose areas can be determined using standard formulae. It is then simply a question of adding the parts together.
For more complicated shapes, there are essentially two options: you can either use uniform laminae and mass or estimate the area using grids.
Uniform Lamina
: Copy the shape onto a sheet (lamina) of material with uniform density. Cut the shape out carefully and measure its mass (or weight). Do the same for a unit square of the lamina.
Then, because the lamina is of uniform density, the ratio of the two areas is the same as the ratio of the two masses.
That is: Area of Shape/Area of Unit Square = Mass of Shape/Mass of Unit Square =
Rearranging, and noting that the area of the Unit Square is, by definition, = 1 sq unit
Area of Shape = Mass of Shape/Mass of Unit Square.
Grid Method
: Copy the shape onto a grid, where each grid square has an area of G square units. Count the number of squares that are fully or mostly inside the shape. Call this number W (for whole). Count the number of squares that are approximately half inside the shape and call this number H (for half). Ignore any square that are less than half in the shape.
Then a reasonable estimate of the area of the shape is G*[W + H/2] square units. There is some arbitrariness about “mostly inside” and “approximately half” but there is no way around that. You will get more accurate results with finer grids, but they will also require much more effort in terms of counting the grid squares.
no. similar polygons do not have the same area. similar just means that they have the same angle measurements and are proportional.
Different polygons have different relationships between perimeter and area. For example, if we assume regular polygons, an equilateral triangle and a square have different perimeters for the same area. If you allow irregular polygons, the variety is even bigger.
That refers to a pattern where the polygons in question, repeated over and over again, cover an area completely.
No, not necessarily.
Polygons and 2 dimensional shapes
Most shapes can be divided into a combination of simple polygons.
no. similar polygons do not have the same area. similar just means that they have the same angle measurements and are proportional.
For instance, you might divide the polygons into triangles, calculate the area of each triangle, and then add everything up.
Different polygons have different relationships between perimeter and area. For example, if we assume regular polygons, an equilateral triangle and a square have different perimeters for the same area. If you allow irregular polygons, the variety is even bigger.
That refers to a pattern where the polygons in question, repeated over and over again, cover an area completely.
No, not necessarily.
Polygons and 2 dimensional shapes
There is insufficient information to answer the question. For a given area, the perimeter depends upon the shape. For a given area, the circle will have the smallest perimeter. For polygons, regular polygons will have a smaller perimeter than an irregular one of the same area. Also, for regular polygons, the greater the number of sides, the smaller the perimeter.
That depends on what polygon you are talking about, and on its dimensions.
There are lots of different types of polygons Polygons are classified into various types based on the number of sides and measures of the angles.: Regular Polygons Irregular Polygons Concave Polygons Convex Polygons Trigons Quadrilateral Polygons Pentagon Polygons Hexagon Polygons Equilateral Polygons Equiangular Polygons
No. For example, a 12x1 and a 4x3 quadrilateral both have an area of 12, but they are not congruent.
no