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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.

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Q: How do you get the area of a polygons?
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Related questions

How does knowing the area of a simple polygons help you determine the area of any shapes?

Most shapes can be divided into a combination of simple polygons.


Does similar polygons always have the same area?

no. similar polygons do not have the same area. similar just means that they have the same angle measurements and are proportional.


How do I find the area of irregular shaped polygons?

For instance, you might divide the polygons into triangles, calculate the area of each triangle, and then add everything up.


How do you find the Perimeter of a polygon with only the area?

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.


What is a tessellation of polygons?

That refers to a pattern where the polygons in question, repeated over and over again, cover an area completely.


Are polygons congruent if they have the same surface area?

No, not necessarily.


What shapes have area?

Polygons and 2 dimensional shapes


If the area is 350square feet what is the perimeter?

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.


What is the answer of Area of Polygons 10.1?

That depends on what polygon you are talking about, and on its dimensions.


what is the name of polygons you given to a shape?

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


Is it true that if two polygons have the same area then they are congruent?

No. For example, a 12x1 and a 4x3 quadrilateral both have an area of 12, but they are not congruent.


Does it matter which way you divide a complex figure int simple polygons to find the area?

no