Question

question rectangle abcd is shown. what is the area of the rectangle in square units?

Explanation:

Step1: Find length of AB using distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(1,6)$ and $B(-2,7)$, we have $x_1 = 1,y_1=6,x_2=-2,y_2 = 7$. Then $AB=\sqrt{(-2 - 1)^2+(7 - 6)^2}=\sqrt{(-3)^2+1^2}=\sqrt{9 + 1}=\sqrt{10}$.

Step2: Find length of BC using distance formula

For points $B(-2,7)$ and $C(-4,1)$, we have $x_1=-2,y_1 = 7,x_2=-4,y_2=1$. Then $BC=\sqrt{(-4+2)^2+(1 - 7)^2}=\sqrt{(-2)^2+(-6)^2}=\sqrt{4 + 36}=\sqrt{40}=2\sqrt{10}$.

Step3: Calculate area of rectangle

The area of a rectangle $A = l\times w$. Here, if we consider $AB$ as length and $BC$ as width, $A=AB\times BC=\sqrt{10}\times2\sqrt{10}=2\times10 = 20$.

Answer:

20