The large side of the rectangular trapezoid is 28 cm, and the acute angle is 30 degrees.

The large side of the rectangular trapezoid is 28 cm, and the acute angle is 30 degrees. Find the area of the trapezoid if a circle can be inscribed into it.

Let’s draw the CH height from the top of the obtuse angle. In a right-angled triangle, the CH leg, the CH leg lies opposite the angle of 30, which means that its length is equal to half the length of the СD hypotenuse. CH = СD / 2 = 28/2 = 14 cm.Then AB = CH = 14 cm.
The sum of the lengths of the lateral sides of the trapezoid is: AB + СD = 14 + 28 = 42 cm.
Since a circle can be inscribed into the trapezoid, AB + СD = BC + AD = 42 cm.
Determine the area of the trapezoid. Savsd = (ВС + AD) * CH / 2 = 42 * 14/2 = 294 cm2.
Answer: The area of the trapezoid is 294 cm2.