Question

find area of square abcd.

Explanation:

Step1: Find the length of side AD

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 \(A(2,5)\) and \(D(- 3,1)\), we have \(x_1 = 2,y_1 = 5,x_2=-3,y_2 = 1\).
\[

$$\begin{align*} AD&=\sqrt{(-3 - 2)^2+(1 - 5)^2}\\ &=\sqrt{(-5)^2+(-4)^2}\\ &=\sqrt{25 + 16}\\ &=\sqrt{41} \end{align*}$$

\]

Step2: Calculate the area of the square

The area of a square is given by \(A=s^2\), where \(s\) is the length of a side. Since \(s = AD=\sqrt{41}\), the area \(A = (\sqrt{41})^2=41\).

Answer:

41