Find the area of the square whose vertices have coordinates (4; 3) (10; 3) (10; 9) (4; 9).

Let the coordinates of the point A (4; 3), B (10; 3).
Knowing the coordinates of the vertices of the square, we determine the length of the side AB.
AB = √ (X ^ 2 – X1) ^ 2 + (Y ^ 2 – Y1) ^ 2 = √ (10 – 4) ^ 2 + (3 – 3) ^ 2 = √36.
AB = 6 cm.
Since, by condition, the quadrilateral AVSD is a square, then AB = BC = SD = AB = 6 cm.
Then its area is equal to: Sawd = AB ^ 2 = 36 cm2.
Answer: The area of the square is 36 cm2.