# NCERT Solutions for Class 7 Maths Chapter 11 – Perimeter and Area

NCERT Solutions for Class 7 Maths Chapter 11 is about another geometrical concept of Perimeter and Area. In Chapter- Perimeter and Area, there are a total of 4 exercises and 40 questions. In NCERT Solutions for Class 7 Maths Chapter 11, we have covered several geometrical shapes like square, rectangle, parallelogram, triangle, circle and the applications of the concept.

Class 7 NCERT Solutions for Chapter 11 ‘Perimeter and Area’ is based on the latest syllabus approved by CBSE. At Instasolv, we provide the most reliable study material for composite mathematics for class 7 solutions chapter 11. Chapter-wise Solutions of NCERT Class 7 Maths Book are also provided below for your ease. In order to score good marks, we highly recommend you to follow Class 7 Maths NCERT Solutions.

Chapter 11 Perimeter and Area, of CBSE NCERT Class 7 Maths Book covers a concept widely used in daily life. For the Maths subject in Class 7, we explain the important elements and summarise each part and subpart of the Chapter. We follow the same sequence as in the book so that it becomes easy to understand and use as a reference.

## NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area: Exercise-Discussion

As discussed above, we will solve a total of 40 questions in this chapter. Through our NCERT Solutions Class 7 Maths for Chapter 11, you get free access to all the answers to each question available in the exercise of this Chapter. Thus you can prepare well for the CBSE exams, and can surely score better.

Below we have discussed all the important topics which will help you understand the questions available in the exercise of Chapter 11:

**Introduction – **Perimeter is the distance around a closed figure. The area is the region of space occupied by the closed figure.

**Squares and Rectangles –**

The perimeter of a regular polygon of n sides is the length of one side x n. A regular polygon has all sides of equal length.

The perimeter of a square where the number of sides is 4: length of one side x 4.

The perimeter of a rectangle which has two smaller sides of equal length, and two larger sides of equal length. The smaller sides are called the breadth of the rectangle denoted by b, larger sides are called the length of the rectangle denoted by l

The perimeter of a rectangle is: 2 x (l+ b)

The area of a square is the square of its side. If the length of a side is l. The area of a square is l x l

Area of a rectangle is l x b

Increasing the perimeter does not necessarily increase the area of a figure. For example, if you take a cut out of a square and cut out, you cut a small rectangle from one side. Since the original cut out has decreased the area of the original square has decreased. The new figure is not a square anymore but the perimeter has increased as compared to the perimeter of the original square.

Increasing the perimeter of a regular shape like a square or rectangle will increase the length of some side at least and also increase the area.

**Triangles as Part of Rectangles**

Cut a square or a rectangle across its diagonals. In each case, you get two right-angled triangles of equal area.

The area of one right-angled triangle is half the area of the square or rectangle from which it is cut respectively which is half of (l x b) or half of (l x l).

This is also how the area of a triangle is calculated (l x b) / 2

**Generalizing for Other Congruent Parts of a Rectangle**

If you cut a rectangle across the two smaller sides (breadth) or across the two longer sides (length) the two parts are half in area of the original rectangle and both parts are congruent to each other.

**Area of a Parallelogram – **Square, and rectangle can be called as special types of parallelograms where all the angles measure ninety degrees. When the measure of the angles is not ninety degrees but the opposite sides are parallel to each other it is called a general parallelogram.

From one vertex if you drop a line at an angle measuring ninety degrees to the opposite side you get a triangle. This line can be called the height of the parallelogram drawn from the base of the parallelogram.

Cut out that triangle and attach it to the other side. The parallelogram has got converted into a rectangle.

The area of the parallelogram, therefore, is the length of its base multiplied by the length of its height. In Chapter 11, you will see a lot of questions based on Area of Parallelogram, thus you can refer to the NCERT Solutions for CBSE Class 7 Chapter 11 by Instasolv.

**Area of a Triangle – **Any regular polygon cut across its diagonals will result in two congruent triangles so the area of any triangle is half the area of the polygon.

Thus, the area of a triangle is half of b x h where b is the length of the base and h is the length of the height.

All congruent triangles are equal in the area but all triangles with equal area need not be congruent.

Remember again, do not forget to mention the unit which may be centimeter, meter, and so on. You can also refer to the NCERT Solutions for Chapter 11 of CBSE Class 7 for step-by-step answers.

**Circle**

**Circumference of a Circle**

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

Let C be the circumference of the circle, D its diameter and R its radius.

The circumference of a circle is always a little more than three times the diameter of that circle. The ratio is fixed and is equal to 22/7 or approximately 3.14. This fixed ratio is called pi.

C = pi x D or 22/7 x D

D – 2 x R

**Area of a Circle**

Area of a circle is equal to half of the circumference multiplied by the radius

Let Area of a Circle be A

A = ½ C x R

A = ½ (2 x 22/7 x R)R

A = 22/7 x R x R

The area of a circle is the constant pi multiplied by the square of its radius.

**Conversion of Units**

Keep note of the units mentioned in the question that are present in the Class 7 Chapter 11 Exercises. To add a little variation to the question different units can also be mentioned. Example length can be given as one meter and breadth can be given as 80 centimeters.

- When questions are solved ensure all the units are matched.
- One meter is equal to hundred centimeters.
- One centimeter is equal to ten millimeters
- One square meter is one meter multiplied by one meter. This can be written as one hundred centimeters multiplied by one hundred centimeters. So one square meter is equal to ten thousand square centimeters.

Make sure you keep the following points in mind while writing the answers.

**Applications**

Consider all the objects that we come across in our daily life which have the shapes we have studied, circle, rectangle, triangle, square. So often we need to find the area or the perimeter of these.

For example, if you want to know the area of your room which is most probably a rectangle, multiply the length and breadth of the room and you get the area.

**Study Tips for NCERT Class 7 Maths Chapter 11: Perimeter and Area**

Students aim to get a high score in the exams. Instasolv recommends that you read chapter 11 Perimeter and Area of CBSE NCERT textbook for Class 7 Maths. Instasolv has provided a simple explanation and summary of each part. This summary can be used as a ready reference.

If any concept is still not understood, ask the experts on the Instasolv app which does not charge any student for this support.

Learning by rote is never recommended by the subject matter experts of Instasolv. There are various types of questions that can be asked. Instasolv recommends that you pay special attention to units and their conversion.

Practice will help improve your speed as well enabling you to attempt all ‘Perimeter and Area’ Class 7 questions and have enough time to check them for any errors. Follow the solutions and tips provided by Instasolv and score high marks in your Maths exam.