# NCERT Solutions and Notes for Class 7 Maths Chapter 9: Perimeter and Area (Free PDF)

In class 6 Maths, we have studied the area and parameters of some regular shapes such as the rectangle and the square. Now, in NCERT Solutions Class 7 Maths Chapter 9, we will learn to determine the area and parameters of some parallelograms and triangles. Later in the chapter, we will also learn to determine the area and circumference of circles. Let us now have a look at the NCERT Solutions Class 7 Maths Chapter 9 Perimeter and Area (PDF).

Download NCERT Class 7 Maths Chapter 9 – Perimeter and Area Notes and Solutions PDF

## NCERT Notes Class 7 Maths Chapter 9 – PDF Available

Check the topic-wise notes for NCERT Solutions Maths Class 7 Chapter 9 below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the e𝑥am hall.

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### Topic 1: Area of a Parallelogram

The area of a parallelogram can be calculated by multiplying the length of its base with height.

Area of a Parallelogram = Base × Height

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### Topic 2: Area of a Triangle

The base and the height of the triangle are the same as the base and the height of the parallelogram, respectively. But the area of a triangle is half the area of the parallelogram of the same height and base. Hence, the area of a triangle can be calculated by multiplying the lengths of its base and height with ½.

Area of a Triangle = ½ × the area of the parallelogram

∴ Area of a Triangle = ½ × (Base × Height)

### Topic 3: Circumference of a Circle

The distance around a circular region is known as its circumference.

Circumference of a circle = 2𝜋r

### Topic 4: Area of a Circle

The area of a circle can be calculated by the following formula.

Area of a circle = 𝜋r2

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Download NCERT Class 7 Maths Chapter 9 – Perimeter and Area Notes and Solutions PDF

## NCERT Solutions of Class 7 Maths Chapter 9: Perimeter and Area- PDF Available!

Below we have provided solutions for NCERT Solutions Class 7 Maths Chapter 9, Perimeter and Area. Go through for answers to some important questions.

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### E𝑥ercise 9.1 Solutions

Q 1. Find the area of the following parallelogram.

Solutions. We know that the area of a parallelogram can be calculated by multiplying the length of its base with height.

In the given parallelogram, base = 7 cm and height = 4 cm.

∴ area of the given parallelogram = base × height = 7 cm × 4 cm = 28 cm2

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Q 2. Find the area of the following triangle.

Solutions. We know that the area of a triangle can be calculated by multiplying the lengths of its base and height with ½.

In the given figure, the height of the triangle is 3 cm long and its base is 4 cm long.

∴ Area of a Triangle = ½ × (Base × Height) = ½ × 3 cm × 4 cm = 6 cm2.

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Q 3. PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find:

1. the area of the parallelogram PQRS
2. QN, if PS = 8 cm

Solutions. We can determine the area of a parallelogram by multiplying the length of its base with height.

1. The base and height of the given parallelogram PQRS are 12 cm and 7.6 cm respectively.

∴ area of the given parallelogram = base × height = 12 cm × 7.6 cm = 91.2 cm2

1. The area of the parallelogram remains the same even if we consider the base and height to be PS and QN respectively.

∴ area of the given parallelogram = base × height

Given: PS (base) = 8 cm and QN (height) = ?

⇒ 91.2 cm2 = 8 cm × QN

⇒ QN = 91.2 cm2/8 cm = 11.4 cm

Thus, the length of the perpendicular QN is 11.4 cm.

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### E𝑥ercise 9.2 Solutions

Q 1. Find the circumference of the circle with a radius 14 cm.

Solutions. We know that the circumference of a circle is 2𝜋r.

So, Circumference of a circle = 2𝜋r = 2 × 22/7 × 14 cm = 88 cm

## FAQs

Q.1. What is the area of a parallelogram?

Ans: The area of a parallelogram can be calculated by multiplying the length of its base with height.
– Area of a Parallelogram = Base × Height

Q.2. What is the relation between the area of a parallelogram and the area of a triangle?

Ans: The area of a triangle is half the area of the parallelogram of the same height and base. Hence, the area of a triangle can be calculated by multiplying the lengths of its base and height with ½.

Area of a Triangle = ½ × area of the parallelogram = ½ × (Base × Height)

Q.3. What is the area of a circle?

Ans: The area of a circle can be calculated by the following formula.
Area of a circle = 𝜋r2

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This was all about NCERT Solutions Class 7 Maths Chapter 9, Perimeter and Area in which we studied the Perimeter and Area. Download the NCERT Solutions Class 7 Maths Chapter 9 PDF to ace your e𝑥am preparations. Follow the CBSE Class 7 Maths Solutions and Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 7 Maths.