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13 Ιουλ 2022 · Given the triangle inscribed in an N-sided regular polygon with given side length, formed using any 3 vertices of the polygon, the task is to find the area of this triangle. Examples: Input: N = 6, side = 10 Output: 129.904 Input: N = 8, side = 5 Output: 45.2665 Approach: Consider the 1st example: Given is a 6 sided regular polygon ABCDEF with a tr
The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
7 Οκτ 2019 · The Shoelace Algorithm to find areas of polygons. This is a nice algorithm, formally known as Gauss’s Area formula, which allows you to work out the area of any polygon as long as you know the Cartesian coordinates of the vertices.
5 ημέρες πριν · The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area formula for the area of a simple polygon in terms of the Cartesian coordinates of its vertices (x_1,y_1), ..., (x_n,y_n).
A method for finding the area of any polygon when the coordinates of its vertices are known. (See also: Computer algorithm for finding the area of any polygon.) First, number the vertices in order, going either clockwise or counter-clockwise, starting at any vertex.
25 Ιουν 2014 · Learn how to apply the shoelace algorithm for calculating the area of a simple polygon. Four different ways are shown, the three of which make use of Excel formulas only, while the last one is a custom VBA function.
15 Οκτ 2024 · Given the n + 1 vertices x[0], y[0] .. x[N], y[N] of a simple polygon described in a clockwise direction, then the polygon's area can be calculated by: abs( (sum(x[0]*y[1] + ... x[n-1]*y[n]) + x[N]*y[0]) - (sum(x[1]*y[0] + ... x[n]*y[n-1]) + x[0]*y[N]) ) / 2
