Question

Use determinants to calculate the area of a polygon with the following vertices:

a= [5,11] b= [10,14] c= [16,19] d= [20,6] e= [11,5]

Answer 1

To find the area of a polygon with given vertices using determinants, apply the Surveyor's Formula which involves creating a matrix of the vertices, using a specific formula that relies on multiplying and summing products of coordinates, and then taking half of the absolute value of the result.

Step-by-step explanation:

To calculate the area of a polygon using determinants, you can apply the Surveyor's Formula, which is a method based on the determinants of matrices formed by the coordinates of the vertices. For the given vertices a= [5,11], b= [10,14], c= [16,19], d= [20,6], and e= [11,5], we can set up a matrix such that it repeats the first vertex at the end:

(5, 11)(10, 14)(16, 19)(20, 6)(11, 5)(5, 11) - repeated

Then we use the following formula for the area (A):

A = 1/2 * |(x1*y2 + x2*y3 + ... + xn*y1) - (y1*x2 + y2*x3 + ... + yn*x1)|

Substituting the coordinates into the formula and solving will give us the area of the polygon. The calculation involves multiplying the x-coordinate of each vertex by the y-coordinate of the next vertex, summing those products, and then subtracting the sum of the products of each y-coordinate and the subsequent vertex's x-coordinate. The absolute value is taken to ensure the area is positive, and then it is halved.