Find the area of a rhombus whose vertices have coordinates (1; 2), (1; 6), (-4; 4), (6; 4)

Using the coordinates of the vertices of the rhombus, we determine the lengths of its diagonals.

AC = √ (X2 – X1) ^ 2 + (Y2 – Y1) ^ 2 = √ (6 – (-4)) ^ 2 + (4 – 4) ^ 2) = √100 = 10 cm.

BD = √ (X2 – X1) ^ 2 + (Y2 – Y1) ^ 2 = √ (1 – 1) ^ 2 + (6 – 2) ^ 2) = √16 = 4 cm.

Let’s define the area of a rhombus through the lengths of its diagonals.

Savsd = АС * ВD / 2 = 10 * 4/2 = 20 cm2.

Answer: The area of the rhombus is 20 cm2.