Given the corner points of a triangle (x1, y1), (x2, y2), (x3, y3), compute the area. Hint: The area of the triangle with corner points (0, 0), ( , ), and ( , ) is | · – · | / 2. Complete the following code:
To compute the area of a triangle given its corner points, we can use the formula:
Area = |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))/2|
where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the corner points of the triangle.
To complete the code, we can define a function that takes in the corner points as arguments and returns the area of the triangle. Here is the code:
def calculate_triangle_area(x1, y1, x2, y2, x3, y3):
area = abs((x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))/2)
This function first computes the difference in y-coordinates and the difference in x-coordinates for each pair of corner points. Then, it uses these differences to calculate the signed area of the parallelogram formed by the vectors formed by the corner points. Finally, the absolute value of the signed area is taken to obtain the area of the triangle.
To use this function, you can call it with the coordinates of the corner points as arguments. For example:
triangle_area = calculate_triangle_area(0, 0, x2, y2, x3, y3)
print(“The area of the triangle is:”, triangle_area)
Here, you would replace `x2`, `y2`, `x3`, and `y3` with the actual coordinates of the corner points of your triangle. The function will then calculate the area using the provided formula and print it out.
It is worth noting that the formula assumes that the corner points are given in counterclockwise order. If the points are given in clockwise order, the formula will give the negative of the actual area. To ensure correct results, make sure your corner points are arranged counterclockwise.
In conclusion, the provided code defines a function that computes the area of a triangle given its corner points using the formula for the signed area of the parallelogram formed by the corner points. By supplying the appropriate coordinates to this function, you can easily calculate the area of any triangle.
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