Find the area of a trapezoid whose vertices have coordinates (1; 3), (3; 1), (3; 6), (1; 5).

Let point A (3; 1), B (1; 3), C (1; 5), D (3; 6).

At points A and D, B and C, the X coordinates are equal, therefore, the segments AD and BC are parallel to the ordinate axis, which means they are parallel to each other and are the bases of the trapezoid.

BP = 6 – 1 = 5 cm.

BC = 5 – 3 = 2 cm.

The height of the trapezoid is the distance between the straight lines BP and BC along the abscissa axis.

H = 3 – 1 = 2 cm.

Determine the area of the trapezoid.

Savsd = (AD + BC) * h / 2 = (5 + 2) * 2/2 = 7 cm2.

Answer: The area of the trapezoid is 7 cm2.