Answer:
The area of rectangle is 42 square unit.
Step-by-step explanation:
We are given a rectangle shown in diagram.
We need to find the area of rectangle.
[tex]\text{Area of rectangle }=L\times B[/tex]
First we have to find the L and B of the rectangle.
Using coordinate system find the coordinate of vertex of rectangle.
Using distance formula to find the distance of leg of rectangle.
A(2,-1) B(9,-8) C(12,-5)
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]L=AB=\sqrt{(2-9)^2+(-1+8)^2}=7\sqrt2[/tex]
[tex]B=BC=\sqrt{(12-9)^2+(-5+8)^2}=3\sqrt2[/tex]
[tex]\text{Area of rectangle }=7\sqrt2\times 3\sqrt2 = 42\text{ Square Unit}[/tex]
Hence, The area of rectangle is 42 square unit.
