Answer:
A = 35 square units
Step-by-step explanation:
Formula to calculate the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Length of the segment between A(2, 2) and B(9, 2) = [tex]\sqrt{(9-2)^2+(2-2)^2}[/tex]
= 7 units
Length of the segment between B(9, 2) and C(9, -3) = [tex]\sqrt{(9-9)^2+(2+3)^2}[/tex]
= 5 units
Length of the segment between C(9, -3) and D(2, -3) = [tex]\sqrt{(9-2)^2+(-3+3)^2}[/tex]
= 7 units
Length of the segment between A(2, 2) and D(2, -3) = [tex]\sqrt{(2-2)^2+(2+3)^2}[/tex]
= 5 units
Therefore, given polygon is a rectangle.
Area of the rectangle = length × width
= 7 × 5
= 35 square units
