Question

A rectangle has coordinates A(-4, 3), B(0, 0), C(6, 8), D(2, 11). What is the area of the rectangle?

Answer 1

Any polygon given by a list of 2D vertex coordinates has area given by the shoelace formula.

That's the absolute value of half the sum of the cross products of the sides.  We form the table of the vertices. We include the first vertex at the end, then calculate the cross product of the side, (a,b) then (c,d) gives cross product ad-bc.

         cross product

-4 3  0

0 0   0

6 8    6(11)-8(2) = 66 - 16 = 50

2 11   2(3) - (11)(-4) = 50

-4 3

So the area is (1/2)(50+50) = 50

Answer: 50