In the adjoining figure, ABCD is a trapezium with parallel sides AB = a cm and DC = b cm. E and F are mid-points of the non-parallel sides. The ratio of area of ABFE and area of EFCD is

1. a : b

2. (3a + b) : (a + 3b)

3. (a + 3b) : (3a + b)

4. (2a + b) : (3a + b)

In the adjoining figure, AB || DC and AB ≠ DC. If the diagonals AC and BD of the trapezium ABCD intersect at O, then which of the following statements is not true ?

1. area of △ABC = area of △ABD

2. area of △ACD = area of △BCD

3. area of △OAB = area of △OCD

4. area of △OAD = area of △OBC

In the figure (2) given below, PQRS is a parallelogram formed by drawing lines parallel to the diagonals of a quadrilateral ABCD through its corners. Prove that area of || gm PQRS = 2 × area of quad. ABCD.

In the parallelogram ABCD, P is a point on the side AB and Q is a point on the side BC. Prove that

(i) area of ∆CPD = area of ∆AQD

(ii) area of ∆ADQ = area of ∆APD + area of ∆CPB.