Determine the coordinates of the corners of the rectangle to compute the area of the rectangle using the distance formula (round to the nearest integer).

Answer:The area of rectangle is [tex]72\ units^{2}[/tex]Step-by-step explanation:see the attached figure with letters to better understand the problemLet[tex]A(3.10),B(12,1),C(16,5),D(7,14)[/tex]we know thatThe area of rectangle is equal to[tex]A=(AB)(BC)[/tex]the formula to calculate the distance between two points is equal to [tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex] Find the distance ABwe have[tex]A(3.10),B(12,1)[/tex]substitute in the formula[tex]AB=\sqrt{(1-10)^{2}+(12-3)^{2}}[/tex] [tex]AB=\sqrt{(-9)^{2}+(9)^{2}}[/tex] [tex]AB=\sqrt{162}\ units[/tex] Find the distance BCwe have[tex]B(12,1),C(16,5[/tex]substitute in the formula[tex]BC=\sqrt{(5-1)^{2}+(16-12)^{2}}[/tex] [tex]BC=\sqrt{(4)^{2}+(4)^{2}}[/tex] [tex]BC=\sqrt{32}\ units[/tex] Find the area of rectangle[tex]A=(\sqrt{162})*(\sqrt{32})=72\ units^{2}[/tex]