#### Chapter 15 Areas of Parallelogram and Triangles R.D. Sharma Solutions for Class 9th MCQ's

**Multiple Choice Questions**

1. Two parallelograms are on the same base and between the same parallels. The ratio of their areas is

(a) 1 : 2

(b) 2 : 1

(c) 1 : 1

(d) 3 : 1

2. A triangle and a parallelogram are on the same base and between the same parallels. The ratio of the areas of triangle and parallelogram is

(a) 1 : 1

(b) 1 : 2

(c) 2 : 1

(d) 1 : 3

3. Let ABC be a triangle of area 24 sq. units and PQR be the triangle formed by the mid-points of the sides of Δ ABC. Then the area of ΔPQR is

(a) 12 sq. units

(b) 6 sq. units

(c) 4 sq. units

(d) 3 sq. units

4. The median of a triangle divides it into two

(a) congruent triangle

(b) isosceles triangles

(c) right triangles

(d) triangles of equal areas

Given: A triangle with a median.

Calculation: We know that a ,”median of a triangle divides it into two triangles of equal area.”

Hence the correct answer is option (d).

5. In a △ABC, D, E, F are the mid-points of sides BC, CA and respectively. If ar(△ABC) = 16cm

(a) 4 cm

(b) 8 cm

7. The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 16 cm and 12 cm is:

(a) 28 cm

9. The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is:

(a) a rhombus of area 24 cm

10. The mid-points of the sides of triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to

(a) ar(△ABC)

(b) 1/2 ar(△ABC)

12. Medians of △ABC intersect at G. If ar(△ABC) = cm

(a) 6 cm

(b) 9 cm

14. In Fig. 15.106, ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =

16. In Fig. 15.108, ABCD and FECG are parallelograms equal in area. If ar(△AQE) = 12 cm

(a) 12 cm

17. Diagonal AC and BD of trapezium ABCD, in which AB || DC, intersect each other at O. The triangle which is equal in area of ΔAOD is

(a) ΔAOB

(b) ΔBOC

(c) ΔDOC

(d) ΔADC

19. ABCD is a trapezium with parallel sides AB =a and DC = b. If E and F are mid-points of non-parallel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is

(a) a : b

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

(c) (3a + b) : (a + 3b)

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

(a) 1 : 2

(b) 2 : 1

(c) 1 : 1

(d) 3 : 1

**Solution**

2. A triangle and a parallelogram are on the same base and between the same parallels. The ratio of the areas of triangle and parallelogram is

(a) 1 : 1

(b) 1 : 2

(c) 2 : 1

(d) 1 : 3

**Solution**3. Let ABC be a triangle of area 24 sq. units and PQR be the triangle formed by the mid-points of the sides of Δ ABC. Then the area of ΔPQR is

(a) 12 sq. units

(b) 6 sq. units

(c) 4 sq. units

(d) 3 sq. units

**Solution**4. The median of a triangle divides it into two

(a) congruent triangle

(b) isosceles triangles

(c) right triangles

(d) triangles of equal areas

**Solution**Given: A triangle with a median.

Calculation: We know that a ,”median of a triangle divides it into two triangles of equal area.”

Hence the correct answer is option (d).

5. In a △ABC, D, E, F are the mid-points of sides BC, CA and respectively. If ar(△ABC) = 16cm

^{2}, then ar(trapezium FBCE) =(a) 4 cm

^{2}(b) 8 cm

^{2}
(c) 12 cm

^{2}
(d) 10 cm

^{2}**Solution**
6. ABCD is a parallelogram. P is ant point on CD. If ar(△DPA) = 10 cm

(a) 15 cm^{2}and ar(△APC) 20 cm^{2}, then ar(△APB) =^{2}
(b) 20 cm

^{2}
(c) 35 cm

^{2}
(d) 30 cm

^{2}**Solution**7. The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 16 cm and 12 cm is:

(a) 28 cm

^{2}
(b) 48 cm

^{2}
(c) 96 cm

(d) 24 cm^{2}^{2}

**Solution**

8. A, B, C, D are mide-points of sides of parallelogram PQRS. If ar(PQRS) = 36 cm

(a) 24 cm^{2}, then ar(ABCD) =^{2}
(b) 18 cm

^{2}
(c) 30 cm

^{2}
(d) 36 cm

^{2}

**Solution**9. The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is:

(a) a rhombus of area 24 cm

^{2}
(b) a rectangle of area 24 cm

^{2}
(c) a square of area 26 cm

^{2}
(d) a trapezium of area 36 cm

^{2}**Solution**10. The mid-points of the sides of triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to

(a) ar(△ABC)

(b) 1/2 ar(△ABC)

(c) 1/3 ar(△ABC)

(d) 1/4 ar(△ABC)

**Solution**
11. If AD is median of △ABC and P is a point on AC such that

ar(△ADP) : ar(△ABD) = 2:3, then ar(△PDC) : ar(△ABC)

(a) 1:5

(b) 1:3

(c) 1:6

(d) 3:5

**Solution**12. Medians of △ABC intersect at G. If ar(△ABC) = cm

^{2}, then ar(△BGC) =(a) 6 cm

^{2}(b) 9 cm

^{2}(c) 12 cm^{2}
(d) 18 cm

^{2}**Solution**
13. In a △ABC if D and E are mid-points of BC and AD respectively such that ar(△AEC) = 4 cm

^{2}, then ar(△BEC) =
(a) 4 cm

(b) 6 cm^{2}^{2}
(c) 8 cm

^{2}
(d) 12 cm

^{2}**Solution**

14. In Fig. 15.106, ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =

**Solution**
15. In Fig. 15.107, PQRS is a parallelogram. If X and Y are mid-points of PQ and SR respectively and diagonal Q is joined. The ratio ar(∥gm XQRY) : ar(△QSR) =

(i) 1:4

(ii) 2:1

(iii) 1:2

(iv) 1:1

**Solution**16. In Fig. 15.108, ABCD and FECG are parallelograms equal in area. If ar(△AQE) = 12 cm

^{2}, then ar(∥gm FGBQ) =(a) 12 cm

^{2}
(b) 20 cm

^{2}
(c) 24 cm

^{2}
(d) 36 cm

^{2}**Solution**17. Diagonal AC and BD of trapezium ABCD, in which AB || DC, intersect each other at O. The triangle which is equal in area of ΔAOD is

(a) ΔAOB

(b) ΔBOC

(c) ΔDOC

(d) ΔADC

**Solution**
18. ABCD is a trapezium in which AB∥DC. If ar(ΔABD) = 24 cm

^{2}and AB = 8 cm, then height of △ABC is
(a) 3 cm

(b) 4 cm

(c) 6 cm

(d) 8 cm

**Solution**19. ABCD is a trapezium with parallel sides AB =a and DC = b. If E and F are mid-points of non-parallel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is

(a) a : b

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

(c) (3a + b) : (a + 3b)

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

**Solution**
20. ABCD is a rectangle with O as any point in its interior. If ar(△AOD) = 3 cm

^{2}and ar(△BOC) = 6 cm^{2}, then area of rectangle ABCD is
(a) 9 cm

^{2}
(b) 12 cm

^{2}
(c) 15 cm

^{2}
(d) 18 cm

^{2}**Solution**