In this lecture, we will cover one of the frequently asked questions in coding tests, which is the “Calculating the Area of a Polygon” problem. We will conduct in-depth learning on how to implement an algorithm to calculate the area of a polygon using JavaScript.<\/p>\n
Write a function to calculate the area of a polygon given the coordinates of its vertices. The vertices of the polygon are sorted either in a clockwise or counterclockwise direction, and the vertex coordinates are represented as integers in a two-dimensional coordinate system.<\/p>\n
n<\/code> (3 \u2264 n<\/code> \u2264 1000)<\/li>\n- The coordinates of
n<\/code> vertices (x1<\/sub>, y1<\/sub>), (x2<\/sub>, y2<\/sub>), ..., (xn<\/sub>, yn<\/sub>)<\/code><\/li>\n<\/ul>\nOutput<\/h3>\n
The area of the polygon should be printed rounded to two decimal places.<\/p>\n
Solution Process<\/h2>\n
There are several methods to calculate the area of a polygon. Here, we will use the most common “Shoelace Formula (or Polygon Area Formula)”. This formula allows us to easily calculate the area of a polygon.<\/p>\n
Shoelace Formula<\/h3>\n
For the given vertices (x1<\/sub>, y1<\/sub>), (x2<\/sub>, y2<\/sub>), ..., (xn<\/sub>, yn<\/sub>)<\/code>, the area A<\/code> is calculated as follows:<\/p>\n\nA = (1\/2) * | \u03a3 (xi<\/sub> * yi+1<\/sub> - yi<\/sub> * xi+1<\/sub>) | \n<\/pre>\nHere, i+1<\/code> is set to return to 1 when i<\/code> reaches n<\/code> using modular arithmetic. This formula considers the contributions of all edges of the polygon in calculating the area.<\/p>\nJavaScript Code Implementation<\/h3>\n
Let’s implement the above formula in code. Below is the code written in JavaScript.<\/p>\n
\nfunction calculatePolygonArea(vertices) {\n let n = vertices.length;\n let area = 0;\n\n for (let i = 0; i < n; i++) {\n let x1 = vertices[i][0];\n let y1 = vertices[i][1];\n let x2 = vertices[(i + 1) % n][0];\n let y2 = vertices[(i + 1) % n][1];\n\n area += (x1 * y2) - (y1 * x2);\n }\n\n return Math.abs(area \/ 2).toFixed(2);\n}\n\n\/\/ Example\nlet vertices = [[0, 0], [4, 0], [4, 3], [0, 4]];\nconsole.log(calculatePolygonArea(vertices)); \/\/ 12.00\n<\/code><\/pre>\nCode Explanation<\/h3>\n\n- The
calculatePolygonArea<\/code> function takes an array of vertex coordinates vertices<\/code> as input.<\/li>\n- It calculates the number of polygon vertices
n<\/code>.<\/li>\n- It initializes the area
area<\/code> to 0, then calculates the area for all vertices.<\/li>\n- It adds the contribution to the area using the current vertex
(xi<\/sub>, yi<\/sub>)<\/code> and the next vertex (xi+1<\/sub>, yi+1<\/sub>)<\/code>.<\/li>\n- It connects the last vertex with the first vertex through modulus operation to complete the area calculation.<\/li>\n
- It returns the calculated area rounded to two decimal places.<\/li>\n<\/ul>\n
Test Cases<\/h2>\n
If you have checked the code, let’s add the following test cases.<\/p>\n
\nlet testVertices1 = [[0, 0], [0, 2], [2, 2], [2, 0]]; \/\/ Rectangle\nlet testVertices2 = [[0, 0], [4, 0], [4, 3], [0, 4]]; \/\/ Irregular Polygon\n\nconsole.log(calculatePolygonArea(testVertices1)); \/\/ 4.00\nconsole.log(calculatePolygonArea(testVertices2)); \/\/ 12.00\n<\/code><\/pre>\nConclusion<\/h3>\n
In this lecture, we explored the theory behind calculating the area of a polygon along with an example of its implementation in JavaScript. I believe that understanding the formula to calculate the area of a polygon and implementing it in actual code will help in coding tests.<\/p>\n
The problem of calculating the area of a polygon is frequently asked in real coding tests, so be sure to firmly grasp the basic theories and problem-solving processes. In the next lecture, we will cover another algorithm problem, so I hope for your continued interest.<\/p>\n
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