NCERT Solutions for Class 9 Maths Chapter 9: Areas of parallelograms and triangles

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The NCERT Solutions for Class 9 Mathematics are provided in this article. Areas of Parallelograms And Triangles deal with the area parallelograms and triangles have, and figures present on the same base and between the same parallels.

Class 9 Maths Chapter 9 Areas of Parallelograms And Triangles has a weightage of 14 marks in the Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 9 covers the following important concepts:

Download: NCERT Solutions for Class 9 Mathematics Chapter 9 pdf

NCERT Solutions for Class 9 Mathematics Chapter 9

NCERT Solution

Important Topics in Class 9 Maths Chapter 9 Areas of Parallelograms And Triangles

Important Topics in Class 9 Maths Chapter 9 Areas of Parallelograms And Triangles are elaborated below:

Area of a Paralellogram

The area of a parallelogram can be defined by the region a parallelogram bounds in a respective two-dimensional space.

The Area of a Parallelogram, Area = b × h (sq. units)
Here,

“b” is the base of the parallelogram
“h” is the height of the parallelogram.

Perimeter of a Parallelogram

The Perimeter of parallelogram is the same as the sum of all four sides of the respective parallelogram.

The Perimeter of a Parallelogram:
First, consider a Parallelogram with two adjacent sides, a and b.
Hence, the Perimeter of parallelogram = a + b + c + d
⇒ 2a + 2b = 2(a+b)
⇒ P = 2(a+b).

Area of a Trapezoid Formula

The area of a trapezoid can be defined as its total space covered by the sides. If the length of the sides are known, the area of the trapezoid can be evaluated by splitting it into smaller polygons, including rectangles and triangles.

Example: Determine the area of a trapezoid that has parallel sides 32 cm and 12 cm respectively. The height of the trapezoid is mentioned as 5 cm. Evaluate the area of the trapezoid.

Solution: As per the equation, the following data is known,
a = 32 cm
b = 12 cm
h = 5 cm
Thus, the area of the trapezoid is = A = ½ (a + b) h
A = ½ (32 + 12) × (5)
= ½ (44) × (5)
= 110 cm².

NCERT Solutions for Class 9 Maths Chapter 9 Exercises:

The detailed solutions for all the NCERT Solutions for Areas of Parallelograms and Triangles under different exercises are:

Also Read:

Unit Related Topics
Area of Rectangle	Areas of Parallelograms and Triangles Important Theorems	Trapezoids
Trapezoid Formula	Perimeter of a Trapezoid	Parallelogram Area

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CBSE X Related Questions

1.
In a trapezium $ABCD$, $AB \parallel DC$ and its diagonals intersect at $O$. Prove that \[ \frac{OA}{OC} = \frac{OB}{OD} \]
View Solution
2.
Find length and breadth of a rectangular park whose perimeter is $100 \, \text{m}$ and area is $600 \, \text{m}^2$.
View Solution
3.
Find the smallest value of $p$ for which the quadratic equation $x^2 - 2(p + 1)x + p^2 = 0$ has real roots. Hence, find the roots of the equation so obtained.
View Solution
4.
In $\triangle ABC, DE || BC$. If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm and DB = 3 cm, then value of x is
- 1
- $\frac{1}{2}$
- --1
- $\frac{1}{3}$
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5.
Find the sum of first 20 terms of an A.P. whose n$^{th}$ term is given by $a_n = 5 + 2n$. Can 52 be a term of this A.P. ?
View Solution
6.
Using prime factorisation, find the HCF of 144, 180 and 192.
View Solution

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NCERT Solutions for Class 9 Maths Chapter 9: Areas of parallelograms and triangles

NCERT Solutions for Class 9 Mathematics Chapter 9

Important Topics in Class 9 Maths Chapter 9 Areas of Parallelograms And Triangles

Area of a Paralellogram

Perimeter of a Parallelogram

Area of a Trapezoid Formula

NCERT Solutions for Class 9 Maths Chapter 9 Exercises:

CBSE X Related Questions

1.
In a trapezium \(ABCD\), \(AB \parallel DC\) and its diagonals intersect at \(O\). Prove that \[ \frac{OA}{OC} = \frac{OB}{OD} \]

2.
Find length and breadth of a rectangular park whose perimeter is \(100 \, \text{m}\) and area is \(600 \, \text{m}^2\).

3.
Find the smallest value of $p$ for which the quadratic equation $x^2 - 2(p + 1)x + p^2 = 0$ has real roots. Hence, find the roots of the equation so obtained.

4.
In \(\triangle ABC, DE || BC\). If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm and DB = 3 cm, then value of x is

5.
Find the sum of first 20 terms of an A.P. whose n\(^{th}\) term is given by \(a_n = 5 + 2n\). Can 52 be a term of this A.P. ?

6.
Using prime factorisation, find the HCF of 144, 180 and 192.

Similar Mathematics Concepts

Comments

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NCERT Solutions for Class 9 Maths Chapter 9: Areas of parallelograms and triangles

NCERT Solutions for Class 9 Mathematics Chapter 9

Important Topics in Class 9 Maths Chapter 9 Areas of Parallelograms And Triangles

Area of a Paralellogram

Perimeter of a Parallelogram

Area of a Trapezoid Formula

NCERT Solutions for Class 9 Maths Chapter 9 Exercises:

CBSE X Related Questions

1.In a trapezium \(ABCD\), \(AB \parallel DC\) and its diagonals intersect at \(O\). Prove that \[ \frac{OA}{OC} = \frac{OB}{OD} \]

2.Find length and breadth of a rectangular park whose perimeter is \(100 \, \text{m}\) and area is \(600 \, \text{m}^2\).

3.Find the smallest value of $p$ for which the quadratic equation $x^2 - 2(p + 1)x + p^2 = 0$ has real roots. Hence, find the roots of the equation so obtained.

4.In \(\triangle ABC, DE || BC\). If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm and DB = 3 cm, then value of x is

5.Find the sum of first 20 terms of an A.P. whose n\(^{th}\) term is given by \(a_n = 5 + 2n\). Can 52 be a term of this A.P. ?

6.Using prime factorisation, find the HCF of 144, 180 and 192.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
In a trapezium \(ABCD\), \(AB \parallel DC\) and its diagonals intersect at \(O\). Prove that \[ \frac{OA}{OC} = \frac{OB}{OD} \]

2.
Find length and breadth of a rectangular park whose perimeter is \(100 \, \text{m}\) and area is \(600 \, \text{m}^2\).

3.
Find the smallest value of $p$ for which the quadratic equation $x^2 - 2(p + 1)x + p^2 = 0$ has real roots. Hence, find the roots of the equation so obtained.

4.
In \(\triangle ABC, DE || BC\). If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm and DB = 3 cm, then value of x is

5.
Find the sum of first 20 terms of an A.P. whose n\(^{th}\) term is given by \(a_n = 5 + 2n\). Can 52 be a term of this A.P. ?

6.
Using prime factorisation, find the HCF of 144, 180 and 192.