Answer: A = 39
Step-by-step explanation:
To find the area of this rectangle, we will find the length of two adjacent sides and multiply them together using the formula for the area of a rectangle.
A = LW
To find the length and width, we can use the distance formula.
[tex]\displaystyle ST=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}=\sqrt{(12-9)^2 +(1-3)^2}=\sqrt{13}[/tex]
[tex]\displaystyle RS=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}=\sqrt{(3-9)^2 +(-6-3)^2}=\sqrt{117}[/tex]
Next, substitute these into the formula. Then, simplify.
A = LW
A = (ST)(RS)
[tex]A = \sqrt{13} *\sqrt{117}[/tex]
[tex]A = \sqrt{13}*3 \sqrt{13}[/tex]
A = 13 * 3
A = 39
