**Learn how to calculate the area of a square and rectangle. Math lesson for kids**

# How to calculate the area of a polygon

You will need

- - twine;
- - tape measure;
- - compasses;
- - ruler;
- - calculator.

Instruction

To calculate the area of an arbitrary polygon, mark an arbitrary point inside it, and then connect it to each vertex. If the polygon is not convex, select a point so that the line segments do not intersect the sides of the shape. For example, if a polygon is the outer boundary of a "star", then the point should be noted not in the "ray" of the star, but in its center.

Now measure the lengths of the sides in each of the resulting triangles. After that, use the formula of Gerona and calculate the area of each of them. The sum of the areas of all triangles will be the required area of the polygon.

If the shape of a polygon has a very large area, for example, a land plot, it will be quite problematic to draw the required lengths. Therefore, in this case, proceed as follows: drive a peg into the center of the polygon and stretch a piece of string from it to each vertex.Then measure and record in a strict sequence the lengths of all segments. Similarly, measure the sides of the polygon itself by pulling the string between adjacent vertices.

To use the Heron formula, first calculate the half perimeter of each triangle using the formula:

p = ½ * (a + b + c),

Where:

a, b and c are the lengths of the sides of the triangle,

p - semi-perimeter (standard notation).

Having determined the semi-perimeter of the triangle, substitute the resulting number in the following formula:

S∆ = √ (p * (p-a) * (p-b) * (p-c)),

Where:

S∆ is the area of a triangle.

p = ½ * (a + b + c),

Where:

a, b and c are the lengths of the sides of the triangle,

p - semi-perimeter (standard notation).

Having determined the semi-perimeter of the triangle, substitute the resulting number in the following formula:

S∆ = √ (p * (p-a) * (p-b) * (p-c)),

Where:

S∆ is the area of a triangle.

If the polygon is convex, i.e. If the interior angle does not exceed 180º, then select any vertex of the polygon as the interior point. In this case, the triangles will turn out to be two less, which sometimes can significantly simplify the task of finding the area of the polygon. The system for calculating the areas of the obtained triangles does not differ from that described above.

When solving school tasks and “tasks for ingenuity”, carefully consider the shape of the polygon. Perhaps it will be possible to divide it into several parts, from which it will be possible to fold the "correct" figure, for example, a square.

**Video: Calculating the Area of a Rectangle and Irregular Polygons**

**Images: How to calculate the area of a polygon**

**Images: How to calculate the area of a polygon**

**Images: How to calculate the area of a polygon**