Question

Write an algorithm and flowchart to find the area of regular polygon

Answer 1

Answer:

If you know the coordinates of the vertices of a polygon, this algorithm can be used to find the area.

Parameters

X, Y Arrays of the x and y coordinates of the vertices, traced in a clockwise direction, starting at any vertex. If you trace them counterclockwise, the result will be correct but have a negative sign.

numPoints The number of vertices

Returns the area of the polygon

The algorithm, in JavaScript:

function polygonArea(X, Y, numPoints)  

{  

area = 0;   // Accumulates area  

j = numPoints-1;  

for (i=0; i<numPoints; i++)

{ area +=  (X[j]+X[i]) * (Y[j]-Y[i]);  

 j = i;  //j is previous vertex to i

}

 return area/2;

}

The algorithm assumes the usual mathematical convention that positive y points upwards. In computer systems where positive y is downwards (most of them) the easiest thing to do is list the vertices counter-clockwise using the "positive y down" coordinates. The two effects then cancel out to produce a positive area.