If line segment EF is 28 and F is halfway through the line, then segment EF will be half of 28. So segment EF=14
Call the point of intersection of the diagonals point X.
Each base is the hypotenuse of an isosceles right triangle whose sides are the diagonals and whose 90° angle is at X. The altitude of that triangle (⊥ distance to the base from X) is half the length of the hypotenuse. Then the height of the trapezoid is half the sum of the base lengths.
The area of the trapezoid is the product of the height and half the sum of the base lengths, hence is the square of half the sum of the base lengths.
... Area = ((16 cm +30 cm)/2)² = (23 cm)² = 529 cm²
If anything is not clear, just ask me.
The square root of 10 because
sqrt(10) ^2 * 3.14 =
10*3.14 = 31.4