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

In which of the following, you find two polygons on the same base and between the same parallels?

1.

2.

3.

4.

In the figure, ABCD is a trapezium with parallel sides AB = x and CD = y. E and F are mid-points of the non-parallel sides AD and BC respectively. The ratio of ar (ABFE) and ar (EFCD) is :

1. x : y

2. (3x + y) : (x + 3y)

3. (x + 3y) : (3x + y)

4. (2x + y) : (3x + y)