P and Q are two points on the side DC of a ∥ gm ABCD. If the area of ΔPAB is 10 cm², then the area of ΔQAB is :

1. 5 cm²

2. 10 cm²

3. 15 cm²

4. 20 cm²

Two diagonals of a parallelogram ABCD intersect at O. If the area of the parallelogram is 20 cm², then the area of ΔAOB is :

1. 20 cm²

2. 15 cm²

3. 10 cm²

4. 5 cm²

Case Study :

A farmer was having a field in the form of a parallelogram ABCD. He divided the field into several parts by taking a point X on the side CD and joining it to vertices A and B. The farmer sowed wheat and pulses in equal portions of the field separately.

Based on the above information, answer the following questions :

1. By joining XA and XB, the field has been divided into how many parts?
(a) 2
(b) 3
(c) 4
(d) 5

2. The shapes of the parts obtained above are :
(a) triangles
(b) rectangles
(c) one triangle two squares
(d) none of these

3. Area of ΔXAB is equal to :
(a) area of parallelogram ABCD
(b) $\dfrac{1}{2}$ area of parallelogram ABCD
(c) area of ΔADX + area of ΔBCX
(d) both 2. and 3.

4. ΔABX and parallelogram ABCD are :
(a) On the same base DC
(b) On the same base AB and between the same parallels BC and AD
(c) On the same base AB and between the same parallels AB and CD
(d) On the same base CD and between the same parallels AB and CD

5.If instead of taking point X on side CD, the farmer takes a point Y on side BC and joins YA and YD, then :
(a) area of ΔADY = area of ΔABY + area of ΔDCY
(b) area of ΔADY = $\dfrac{1}{3}$ area of parallelogram ABCD
(c) area of ΔADY = area of ΔABY
(d) area of ΔADY = area of ΔDCY

Assertion (A) : In the figure, ABCD is a parallelogram. Area of ΔABD = $\dfrac{1}{2}$ Area of ∥ gm ABCD.

Reason (R) : If a triangle and a parallelogram are on the same base and between the same parallels, then area of the triangle is equal to half of the area of the parallelogram.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false