A diagonal is drawn in a rectangle with sides of 12 and 6 cm. find the area of the resulting triangles.

1) First, we find the area of a rectangle with sides of 12 cm and 6 cm.
To calculate the area of a rectangle, you need to multiply the length by the width of the rectangle.
S = 12 cm * 6 cm = 12 * 6 cm ^ 2 = 10 * 6 cm ^ 2 + 2 * 6 cm ^ 2 = 60 cm ^ 2 + 21 cm ^ 2 = 72 cm ^ 2.
2) The diagonal of the rectangle divides the rectangle into 2 equal triangles. This means that the area of one triangle is equal to half of the rectangle.
S tr = 1/2 * S = 1/2 * 72 cm ^ 2 = 72/2 cm ^ 2 = 70/2 cm ^ 2 + 2/2 cm ^ 2 = 35 cm ^ 2 + 1 cm ^ 2 = 36 cm ^ 2.
Answer: the area of the triangles is 36 cm ^ 2.