{"id":23845,"date":"2021-10-05T20:28:41","date_gmt":"2021-10-05T14:58:41","guid":{"rendered":"https:\/\/python-programs.com\/?p=23845"},"modified":"2021-11-22T18:33:25","modified_gmt":"2021-11-22T13:03:25","slug":"python-program-for-area-of-a-polygon-with-given-n-ordered-vertices","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-for-area-of-a-polygon-with-given-n-ordered-vertices\/","title":{"rendered":"Python Program for Area of a Polygon with Given n Ordered Vertices"},"content":{"rendered":"<p>Given two lists which are the ordered coordinates of a polygon with n vertices, the task is to find the area of a given polygon.<\/p>\n<p>Ordered means that the coordinates are given either clockwise or anticlockwise from the first vertex to the last.<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given x-coordinates list = [1, 5, 1]\r\nGiven y-coordinates list = [6, 4, 3]<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The Area of the given polygon for the given n ordered vertices :\r\n6<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given x-coordinates list = [2, 3, 3, 1]\r\nGiven y-coordinates list = [9, 2, 1, 2]<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The Area of the given polygon for the given n ordered vertices :\r\n8<\/pre>\n<h2>Program for Area of a Polygon with Given n Ordered Vertices in Python<\/h2>\n<p>Below are the ways to find the area of a given polygon for the given n ordered vertices in python:<\/p>\n<ul>\n<li><a href=\"#Using_Mathematical_Formula_(Static_Input)\">Using Mathematical Formula (Static Input)<\/a><\/li>\n<li><a href=\"#Using_Mathematical_Formula_(User_Input)\">Using Mathematical Formula (User Input)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_Mathematical_Formula_(Static_Input)\">Method #1: Using Mathematical Formula (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the x-coordinates list as static input and store it in a variable.<\/li>\n<li>Give the y-coordinates list as static input and store it in another variable.<\/li>\n<li>Calculate the length of the given x-coordinates list and store it in another variable.<\/li>\n<li>Take a variable say <strong>polygn_area<\/strong> and initialize its value to 0.<\/li>\n<li>Subtract 1 from the above x-coordinates list length and store it in another variable say k .<\/li>\n<li>Loop till the length of the given x-coordinates list using the for loop.<\/li>\n<li>Calculate the area of the polygon using the above given mathematical formula and add it to the above-initialized variable <strong>polygn_area\u00a0<\/strong><\/li>\n<li>Assign the value of the iterator to the k which is the previous vertex to the iterator.<\/li>\n<li>Divide the above <strong>polygn_area <\/strong>by 2, apply the abs() function to it which gives the absolute value, and convert it to an integer using the int() function.<\/li>\n<li>Store it in another variable.<\/li>\n<li>Print the above result which is the area of the given polygon.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Give the x-coordinates list as static input and store it in a variable.\r\na = [1, 5, 1]\r\n# Give the y-coordinates list as static input and store it in another variable.\r\nb = [6, 4, 3]\r\n# Calculate the length of the given x-coordinates list and store it in another variable.\r\nlst_lengt = len(a)\r\n# Take a variable say polygn_area and initialize its value to 0.\r\npolygn_area = 0\r\n# Subtract 1 from the above x-coordinates list length and store it in another variable\r\n# say k .\r\nk = lst_lengt - 1\r\nprint(\"The Area of the given polygon for the given n ordered vertices :\")\r\n# Loop till the length of the given x-coordinates list using the for loop.\r\nfor itr in range(0, lst_lengt):\r\n    # Calculate the area of the polygon using the above given mathematical formula and\r\n    # add it to the above-initialized variable polygn_area.\r\n    polygn_area += (a[k] + a[itr]) * (b[k] - b[itr])\r\n    # Assign the value of the iterator to the k which is the previous vertex\r\n    # to the iterator.\r\n    k = itr\r\n# Divide the above polygn_area by 2, apply the abs() function to it which gives\r\n# the absolute value, and convert it to an integer using the int() function.\r\n# Store it in another variable.\r\nrslt = int(abs(polygn_area \/ 2.0))\r\n# Print the above result which is the area of the given polygon.\r\nprint(rslt)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The Area of the given polygon for the given n ordered vertices :\r\n6<\/pre>\n<h3 id=\"Using_Mathematical_Formula_(User_Input)\">Method #2: Using Mathematical Formula (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the x-coordinates list as user input using list(),map(),input(),and split() functions.<\/li>\n<li>Store it in a variable.<\/li>\n<li>Give the y-coordinates list as user input using list(),map(),input(),and split() functions.<\/li>\n<li>Store it in another variable.<\/li>\n<li>Calculate the length of the given x-coordinates list and store it in another variable.<\/li>\n<li>Take a variable say <strong>polygn_area<\/strong> and initialize its value to 0.<\/li>\n<li>Subtract 1 from the above x-coordinates list length and store it in another variable say k .<\/li>\n<li>Loop till the length of the given x-coordinates list using the for loop.<\/li>\n<li>Calculate the area of the polygon using the above given mathematical formula and add it to the above-initialized variable <strong>polygn_area\u00a0<\/strong><\/li>\n<li>Assign the value of the iterator to the k which is the previous vertex to the iterator.<\/li>\n<li>Divide the above <strong>polygn_area <\/strong>by 2, apply the abs() function to it which gives the absolute value, and convert it to an integer using the int() function.<\/li>\n<li>Store it in another variable.<\/li>\n<li>Print the above result which is the area of the given polygon.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Give the x-coordinates list as user input using list(),map(),input(),and split() functions.\r\n# Store it in a variable.\r\na = list(map(int, input( 'Enter some random List Elements separated by spaces = ').split()))\r\n# Give the y-coordinates list as user input using list(),map(),input(),and split() functions.\r\n# Store it in another variable.\r\nb = list(map(int, input( 'Enter some random List Elements separated by spaces = ').split()))\r\n# Calculate the length of the given x-coordinates list and store it in another variable.\r\nlst_lengt = len(a)\r\n# Take a variable say polygn_area and initialize its value to 0.\r\npolygn_area = 0\r\n# Subtract 1 from the above x-coordinates list length and store it in another variable\r\n# say k .\r\nk = lst_lengt - 1\r\nprint(\"The Area of the given polygon for the given n ordered vertices :\")\r\n# Loop till the length of the given x-coordinates list using the for loop.\r\nfor itr in range(0, lst_lengt):\r\n    # Calculate the area of the polygon using the above given mathematical formula and\r\n    # add it to the above-initialized variable polygn_area.\r\n    polygn_area += (a[k] + a[itr]) * (b[k] - b[itr])\r\n    # Assign the value of the iterator to the k which is the previous vertex\r\n    # to the iterator.\r\n    k = itr\r\n# Divide the above polygn_area by 2, apply the abs() function to it which gives\r\n# the absolute value, and convert it to an integer using the int() function.\r\n# Store it in another variable.\r\nrslt = int(abs(polygn_area \/ 2.0))\r\n# Print the above result which is the area of the given polygon.\r\nprint(rslt)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random List Elements separated by spaces = 2 3 3 1\r\nEnter some random List Elements separated by spaces = 9 2 1 2\r\nThe Area of the given polygon for the given n ordered vertices :\r\n8<\/pre>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given two lists which are the ordered coordinates of a polygon with n vertices, the task is to find the area of a given polygon. Ordered means that the coordinates are given either clockwise or anticlockwise from the first vertex to the last. Examples: Example1: Input: Given x-coordinates list = [1, 5, 1] Given y-coordinates &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-for-area-of-a-polygon-with-given-n-ordered-vertices\/\"> <span class=\"screen-reader-text\">Python Program for Area of a Polygon with Given n Ordered Vertices<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":23969,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python Program for Area of a Polygon with Given n Ordered Vertices - Python Programs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/python-programs.com\/python-program-for-area-of-a-polygon-with-given-n-ordered-vertices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program for Area of a Polygon with Given n Ordered Vertices - Python Programs\" \/>\n<meta property=\"og:description\" content=\"Given two lists which are the ordered coordinates of a polygon with n vertices, the task is to find the area of a given polygon. 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Ordered means that the coordinates are given either clockwise or anticlockwise from the first vertex to the last. 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