Question

what is the area of a parallelogram if the coordinates of its vertices are (0,-2) (3,2) (8,2) and (5,-2)?

Answer 1

A common strategy when finding the area of a polygon while you're only given the coordinates is to employ the shoelace formula. To start, we have to order the coordinates either clockwise or counterclockwise ( see attatched for a drawing). So, now we can order the coordinates counterclockwise, adding the first entry again at the end (see second attatchment) Now we can use shoelace. When going left to right, we'll multiply the numbers and they will be positive, and we'll make those numbers negative. ( see third attatchment). After we add them up and subtract when necessary, we'll divide the whole thing by 2. Here's the math:

$\frac{(0*-2+5*2+8*2+3*-2)-(0*2+2*3+8*-2+5*-2)}{2}=20$