Question

Problem 3.5. Compute the area of an arbitrary triangle An arbitrary tri- angle can be described by the coordinates of its three vertices: (r1, yl), (x2, y2), (r3, y3), numbered in a counterclockwise direction. The area of the triangle is given by the formula GT2y3 – 1342 – 11y3 + *3y1 +*1¥2 – 12y1| Write a function t riangle_area(vertices) that returns the area of a triangle whose vertices are specified by the argument vertices, which is a nested list of the vertex coordinates. Make sure your implementation passes the following test function, which also illustrates how the triangle_area function works: def test triangle_area(): Verify the area of a triangle with vertices (0,0), (1,0), and (0,2). v1 = (0,0); v3 = (0,2) v2 = (1,0); [v1, v2, v3] vertices = expected computed = triangle area(vertices) tol = 1E-14 success = abs (expected computed) < tol msg = f"computed area={computed} != {expected}(expected)" assert success, msg Language: python

Answer 1

Here is the completed code for this problem. Comments are included, go through it, learn how things work and let me know if you have any doubts or if you need anything to change. If you are satisfied with the solution, please rate the answer. Thanks

Note: Please maintain proper code spacing (indentation), just copy the code part and paste it in your compiler/IDE directly, no modifications required.

#code

#required method
def triangle_area(vertices):
    #parsing each vertex into individual x,y coordinates
    x1, y1 = vertices[0]
    x2, y2 = vertices[1]
    x3, y3 = vertices[2]
    #applying the equation to find the area and returning it
    A = 0.5 * (x2 * y3 - x3 * y2 - x1 * y3 + x3 * y1 + x1 * y2 - x2 * y1)
    return A