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 problem
Let
[tex]A(3.10),B(12,1),C(16,5),D(7,14)[/tex]
we know that
The 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 AB
we 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 BC
we 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]
