NCERT Exemplar solutions for Mathematics Class 9 chapter 9 - Areas of Parallelograms & Triangles [Latest edition]

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NCERT Exemplar solutions for Mathematics Class 9 chapter 9 - Areas of Parallelograms & Triangles - Shaalaa.com
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Solutions for Chapter 9: Areas of Parallelograms & Triangles

Below listed, you can find solutions for Chapter 9 of CBSE NCERT Exemplar for Mathematics Class 9.


Exercise 9.1Exercise 9.2Exercise 9.3Exercise 9.4
Exercise 9.1 [Pages 85 - 87]

NCERT Exemplar solutions for Mathematics Class 9 Chapter 9 Areas of Parallelograms & Triangles Exercise 9.1 [Pages 85 - 87]

Choose the correct alternative:

Exercise 9.1 | Q 1 | Page 85

The median of a triangle divides it into two ______.

  • Triangles of equal area

  • Congruent triangles

  •  right triangles

  • Isosceles triangles

Exercise 9.1 | Q 2 | Page 85

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

Exercise 9.1 | Q 3 | Page 86

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

  • a rhombus of area 24 cm2

  • a rectangle of area 24 cm2

  • a square of area 26 cm2

  • a trapezium of area 14 cm2

Exercise 9.1 | Q 4 | Page 86

In figure, the area of parallelogram ABCD is ______.

  • AB × BM

  • BC × BN

  • DC × DL

  • AD × DL

Exercise 9.1 | Q 5 | Page 86

In figure if parallelogram ABCD and rectangle ABEF are of equal area, then ______.

  • Perimeter of ABCD = Perimeter of ABEM

  • Perimeter of ABCD < Perimeter of ABEM

  • Perimeter of ABCD > Perimeter of ABEM

  • Perimeter of ABCD = `1/2` (Perimeter of ABEM)

Exercise 9.1 | Q 6 | Page 87

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

  • `1/2` ar (ABC)

  • `1/3` ar (ABC)
  • `1/4` ar (ABC)
  • ar (ABC)
Exercise 9.1 | Q 7 | Page 87

Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is ______.

  • 1:2

  • 1:1

  • 2:1

  • 3:1

Exercise 9.1 | Q 8 | Page 87

ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD ______.

  • Is a rectangle

  • Is always a rhombus

  • Is a parallelogram

  • Need not be any of (A), (B) or (C)

Exercise 9.1 | Q 9 | Page 87

If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram is ______.

  • 1:3

  • 1:2

  • 3:1

  • 1:4

Exercise 9.1 | Q 10 | Page 87

ABCD is a trapezium with parallel sides AB = a cm and DC = b cm (figure). E and F are the mid-points of the non-parallel sides. The ratio of ar (ABFE) and ar (EFCD) is ______.

  • a : b

  • (3a + b) : (a + 3b)

  • (a + 3b) : (3a + b)

  • (2a + b) : (3a + b)

Exercise 9.2 [Page 88]

NCERT Exemplar solutions for Mathematics Class 9 Chapter 9 Areas of Parallelograms & Triangles Exercise 9.2 [Page 88]

State whether the following statement is True or False:

Exercise 9.2 | Q 1 | Page 88

ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 24 cm2, then ar (ABC) = 24 cm2.

  • True

  • False

Exercise 9.2 | Q 2 | Page 88

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then ar (PAS) = 30 cm2.

  • True

  • False

Exercise 9.2 | Q 3 | Page 88

PQRS is a parallelogram whose area is 180 cm2 and A is any point on the diagonal QS. The area of ∆ ASR = 90 cm2.

  • True

  • False

Exercise 9.2 | Q 4 | Page 88

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then ar (BDE) = `1/4` ar (ABC).

  • True

  • False

Exercise 9.2 | Q 5 | Page 88

In figure, ABCD and EFGD are two parallelograms and G is the mid-point of CD. Then ar (DPC) = `1/2` ar(EFGD).

  • True

  • False

Exercise 9.3 [Pages 89 - 92]

NCERT Exemplar solutions for Mathematics Class 9 Chapter 9 Areas of Parallelograms & Triangles Exercise 9.3 [Pages 89 - 92]

Exercise 9.3 | Q 1 | Page 89

In figure, PSDA is a parallelogram. Points Q and R are taken on PS such that PQ = QR = RS and PA || QB || RC. Prove that ar (PQE) = ar (CFD).

Exercise 9.3 | Q 2 | Page 90

X and Y are points on the side LN of the triangle LMN such that LX = XY = YN. Through X, a line is drawn parallel to LM to meet MN at Z (See figure). Prove that ar (LZY) = ar (MZYX)

Exercise 9.3 | Q 3.(i) | Page 90

The area of the parallelogram ABCD is 90 cm2 (see figure). Find ar (ΔBEF)

Exercise 9.3 | Q 3.(ii) | Page 90

The area of the parallelogram ABCD is 90 cm2 (see figure). Find ar (ΔABD)

Exercise 9.3 | Q 3.(iii) | Page 90

The area of the parallelogram ABCD is 90 cm2 (see figure). Find ar (ΔBEF)

Exercise 9.3 | Q 4 | Page 90

In ∆ABC, D is the mid-point of AB and P is any point on BC. If CQ || PD meets AB in Q (figure), then prove that ar (BPQ) = `1/2` ar(∆ABC).

Exercise 9.3 | Q 5 | Page 90

ABCD is a square. E and F are respectively the midpoints of BC and CD. If R is the mid-point of EF (figure), prove that ar (AER) = ar (AFR)

Exercise 9.3 | Q 6 | Page 91

O is any point on the diagonal PR of a parallelogram PQRS (figure). Prove that ar (PSO) = ar (PQO).

Exercise 9.3 | Q 7 | Page 91

ABCD is a parallelogram in which BC is produced to E such that CE = BC (figure). AE intersects CD at F. If ar (DFB) = 3 cm2, find the area of the parallelogram ABCD.

Exercise 9.3 | Q 8 | Page 91

In trapezium ABCD, AB || DC and L is the mid-point of BC. Through L, a line PQ || AD has been drawn which meets AB in P and DC produced in Q (figure). Prove that ar (ABCD) = ar (APQD)

Exercise 9.3 | Q 9 | Page 92

If the mid-points of the sides of a quadrilateral are joined in order, prove that the area of the parallelogram so formed will be half of the area of the given quadrilateral (figure).

Exercise 9.4 [Pages 94 - 96]

NCERT Exemplar solutions for Mathematics Class 9 Chapter 9 Areas of Parallelograms & Triangles Exercise 9.4 [Pages 94 - 96]

Exercise 9.4 | Q 1 | Page 94

A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that ar (ADF) = ar (ABFC)

Exercise 9.4 | Q 2 | Page 94

The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

Exercise 9.4 | Q 3 | Page 94

The medians BE and CF of a triangle ABC intersect at G. Prove that the area of ∆GBC = area of the quadrilateral AFGE.

Exercise 9.4 | Q 4 | Page 95

In figure, CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY).

Exercise 9.4 | Q 5 | Page 95

ABCD is a trapezium in which AB || DC, DC = 30 cm and AB = 50 cm. If X and Y are, respectively the mid-points of AD and BC, prove that ar (DCYX) = `7/9` ar (XYBA

Exercise 9.4 | Q 6 | Page 95

In ∆ABC, if L and M are the points on AB and AC, respectively such that LM || BC. Prove that ar (LOB) = ar (MOC)

Exercise 9.4 | Q 7 | Page 95

In figure, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (APQ)

Exercise 9.4 | Q 8 | Page 96

If the medians of a ∆ ABC intersect at G, show that ar (AGB) = ar (AGC) = ar (BGC) = `1/3` ar (ABC)

Exercise 9.4 | Q 9 | Page 96

In figure, X and Y are the mid-points of AC and AB respectively, QP || BC and CYQ and BXP are straight lines. Prove that ar (ABP) = ar (ACQ).

Exercise 9.4 | Q 10 | Page 96

In figure, ABCD and AEFD are two parallelograms. Prove that ar (PEA) = ar (QFD).

Solutions for Chapter 9: Areas of Parallelograms & Triangles

Exercise 9.1Exercise 9.2Exercise 9.3Exercise 9.4
NCERT Exemplar solutions for Mathematics Class 9 chapter 9 - Areas of Parallelograms & Triangles - Shaalaa.com

NCERT Exemplar solutions for Mathematics Class 9 chapter 9 - Areas of Parallelograms & Triangles

Shaalaa.com has the CBSE Mathematics Mathematics Class 9 CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT Exemplar solutions for Mathematics Mathematics Class 9 CBSE 9 (Areas of Parallelograms & Triangles) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT Exemplar textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Mathematics Class 9 chapter 9 Areas of Parallelograms & Triangles are Corollary: Triangles on the same base and between the same parallels are equal in area., Corollary: A rectangle and a parallelogram on the same base and between the same parallels are equal in area., Theorem: Parallelograms on the Same Base and Between the Same Parallels., Concept of Area.

Using NCERT Exemplar Mathematics Class 9 solutions Areas of Parallelograms & Triangles exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Exemplar Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics Class 9 students prefer NCERT Exemplar Textbook Solutions to score more in exams.

Get the free view of Chapter 9, Areas of Parallelograms & Triangles Mathematics Class 9 additional questions for Mathematics Mathematics Class 9 CBSE, and you can use Shaalaa.com to keep it handy for your exam preparation.

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