Calculate the area of the trapezoid ABCD, if the length of its midline is 10cm

Calculate the area of the trapezoid ABCD, if the length of its midline is 10cm, the length of the side AB is 6cm, the angle ABC is 150 degrees at the base.

Let’s draw the height of the ВН trapezoid.

Triangle AВН is rectangular, in which we determine the magnitude of the acute angle AВН.

Angle AВН = ABC – ВСН = 150 – 90 = 60, then angle ВAН = 180 – 90 – 60 = 30.

The leg AH of a right-angled triangle ABН lies opposite an angle of 30, then BH = AB / 2 = 6/2 = 3 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2.

Since (ВС + АD) / 2 = КР, according to the formula of the middle line, then Savsd = КР * ВН = 10 * 3 = 30 cm2.

Answer: The area of the trapezoid is 30 cm2