The Perimeter Of A Polygon: How To Calculate Correctly | The Science



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The perimeter of a polygon: how to calculate correctly

The line bounding the occupied area of ​​the flat geometric figure, called the perimeter. In this polygon polyline it includes all parties, therefore, to calculate the length of the perimeter need to know the length of each side. In a regular polygon the length of segments between the vertices of the same, which simplifies the calculations.

The perimeter of a polygon: how to calculate correctly

Instruction perimeter of a polygon: how to calculate correctly

Step 1:

To calculate the length of the perimeter of the irregular polygon you would have to figure out possible means the length of each of the parties separately. If this figure is depicted in the drawing, specify the size of the parties, for example, using a ruler and add the obtained values ​​- the result is the desired perimeter.

Step 2:

The polygon can be defined in a task the coordinates of its vertices. In this case series, calculate the length of each side. Use the coordinates of points (eg A (X₁, Y₁), B (X₂, Y₂)), limiting segments that are parties to the figures. Find the difference between the coordinates of these two points along each axis (X₁-X₂ and Y₁-Y₂), Lift the values ​​obtained in the square and fold. Then remove the root of the value obtained: √ ((X₁-X₂) ² + (Y₁-Y₂) ²) - this will be the length of the side between the nodes A and B. Repeat this procedure for each pair of adjacent peaks, then fold the calculated lengths of the sides to identify the perimeter length.

Step 3:

If the conditions mentioned problem that the polygon is correct, and given the number of its vertices or sides to find the perimeter of sufficient length calculation only one hand. If you know the coordinates, calculate it in the manner described above, and the resulting increase in the value of the number of times equal to the number of parties to calculate the perimeter.

Step 4:

With the known conditions of tasks including sides (n) of a regular polygon and the diameter (D) described around it circumference, perimeter length (P) can be calculated using trigonometric functions - sinus. The length of the sides define the multiplication of known diameter on the sine of the angle, the value of which is equal to 180 °, divided by the number of sides: D * sin (180 ° / n). To calculate the perimeter, as stated in the previous step, multiply the result by the number of sides: P = D * sin (180 ° / n) * n.

Step 5:

From the known diameter (d) of the circle inscribed in a regular polygon with a predetermined number of nodes (n), it is also possible to define the perimeter (P). In this case, the calculation formula will differ from those described in the previous step only used it a trigonometric function - replace the sine by the tangent: P = d * tg (180 ° / n) * n.