An architect designs a rooflight to allow the sunlight into the hall in the shape of trapezium \(ABCD\) where \(AB\parallel CD\). \(AB=25cm\) and \( CD=58cm\) and the non-parallel sides \(AD=30cm\) and \(BC=30cm\) and height between two parallel sides is \(10cm\). Inside the trapezium the architech designs by joining the midpoints of the non-paralle sides names as \(EF\). A hanglight is suspended at the midpoint of diagonal \(AC\).
Based on the above situation, answer the following questions:
(i) Find the area of the rooflight.
(ii) The architech wants to decor the border of rooflight with metal strip. Then find the length of metal strip required.
(iii) Find the length of \(EO\) by using midpoint theorem.
(iv) If \(\angle A= 75^\circ\), then find the angle of \(\angle D\).