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
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) = 16cm2, then ar(trapezium FBCE) =
(a) 4 cm2
(b) 8 cm2
Solution
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 cm2
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 cm2
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)
Solution
Solution
12. Medians of △ABC intersect at G. If ar(△ABC) = cm2, then ar(△BGC) =
(a) 6 cm2
(b) 9 cm2(c) 12 cm2
Solution
13. In a △ABC if D and E are mid-points of BC and AD respectively such that ar(△AEC) = 4 cm2, then ar(△BEC) =
14. In Fig. 15.106, ABCD is a parallelogram. If AB = 12 cm, AE = 7.5 cm, CF = 15 cm, then AD =
Solution
Solution
16. In Fig. 15.108, ABCD and FECG are parallelograms equal in area. If ar(△AQE) = 12 cm2, then ar(∥gm FGBQ) =
(a) 12 cm2
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
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
Solution
(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) = 16cm2, then ar(trapezium FBCE) =
(a) 4 cm2
(b) 8 cm2
(c) 12 cm2
(d) 10 cm2
Solution
6. ABCD is a parallelogram. P is ant point on CD. If ar(△DPA) = 10 cm2 and ar(△APC) 20 cm2, then ar(△APB) =
(a) 15 cm2
(b) 20 cm2
(c) 35 cm2
(d) 30 cm2
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 cm2
(b) 48 cm2
(c) 96 cm2
(d) 24 cm2
Solution
8. A, B, C, D are mide-points of sides of parallelogram PQRS. If ar(PQRS) = 36 cm2, then ar(ABCD) =
(a) 24 cm2
(b) 18 cm2
(c) 30 cm2
(d) 36 cm2
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 cm2
(b) a rectangle of area 24 cm2
(c) a square of area 26 cm2
(d) a trapezium of area 36 cm2
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) = cm2, then ar(△BGC) =
(a) 6 cm2
(b) 9 cm2(c) 12 cm2
(d) 18 cm2
Solution
13. In a △ABC if D and E are mid-points of BC and AD respectively such that ar(△AEC) = 4 cm2, then ar(△BEC) =
(a) 4 cm2
(b) 6 cm2
(c) 8 cm2
(d) 12 cm2
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 cm2, then ar(∥gm FGBQ) =
(a) 12 cm2
(b) 20 cm2
(c) 24 cm2
(d) 36 cm2
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 cm2 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 cm2 and ar(△BOC) = 6 cm2, then area of rectangle ABCD is
(a) 9 cm2
(b) 12 cm2
(c) 15 cm2
(d) 18 cm2
Solution