[tex]\begin{gathered} A)20m \\ 25m^2 \\ \end{gathered}[/tex]
Explanation
the distance between 2 points, A and B, is given by:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ A(x_1,y_1)andB(x_2,y_2) \end{gathered}[/tex]
Step 1
name the other coordinates for the square
A(7,9)
B(10,5)
C(3,6)
D(6,2)
Step 2
find the distances
1)AB
[tex]\begin{gathered} d=\sqrt[]{(10-7)^2+(5-9)^2} \\ d=\sqrt[]{(3)^2+(-4)^2} \\ d=\sqrt[]{9+16\text{ d= }\sqrt[]{25}} \\ \text{distace AB=5} \end{gathered}[/tex]
AB=5
2) BD
[tex]\begin{gathered} d=\sqrt[]{(6-10)^2+(2-5)^2} \\ d=\sqrt[]{(-4)^2+(-3)^2} \\ d=\sqrt[]{16+9}=\sqrt[]{25} \\ d=5 \end{gathered}[/tex]
DB=5
Step 3
the area of a square is given by
[tex]\begin{gathered} \text{Area}=side^2 \\ \text{replace} \\ \text{Area}=(5m)^2 \\ \text{Area}=25m^2 \end{gathered}[/tex]
Step 4
the perimeter of a square is given by:
[tex]\begin{gathered} \text{Perimeter}=4\cdot\text{ side} \\ \text{replace} \\ \text{Perimeter}=4\cdot\text{ 5 ms} \\ \text{Perimeter}=20\text{ m} \end{gathered}[/tex]
