Chapter Notes - Perimeter and Area

# Perimeter and Area Class 7 Notes Maths Chapter 9

A picture of a garden is given below. You have to cover the boundaries with flowers.

How would you calculate the measurement of the boundaries of the garden?

To find the distance around the boundaries of the garden, you need to calculate the perimeter. To find the perimeter of this rectangle, we add up all the sides.

So we add 16.3m + 16.7m + 16.3m + 16.7m, which is equal to 66m. So, the perimeter of the rectangle is equal to 66m.

Now, if we have to cover the whole garden, how would you calculate the space inside the garden?

To calculate this, we will need to find the area of the garden.

The area is the amount of space inside a shape. For a rectangle, we find the area by multiplying the length by the width.

So area is equal to 16.3m x 16.7m, which is equal to 272.21m2

## Area of Parallelograms

A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length.

To find the area of a parallelogram, you can follow these steps:

• Choose a Base: Select any side of the parallelogram as the base.
• Determine the Height: Draw a perpendicular line from the opposite vertex to the chosen base. This perpendicular line is called the height.
• Calculate Area: The area of the parallelogram is given by the formula: Area = Base × Height.
h = Height of Parallelogram
b = Base of Parallelogram

If you have a parallelogram ABCD, where AB is the base and DE is the height (perpendicular to AB), then the area would be given by:
Parallelogram ABCD

Area=Base×Height=��×Area of parallelogram ABCD Base × Height= AB x DE

Question for Chapter Notes - Perimeter and Area
Try yourself:What is the formula to calculate the area of a parallelogram?

Example 1: Find the area of the following parallelograms:

Ans: Base = 8 cm

Height = 3.5 cm

Area of parallelogram = Base × Height

Area of parallelogram = 8 cm x 3.5 cm = 28 cm2

Ans: Base = 8 cm

Height = 2.5 cm

Area of parallelogram = Base × Height

Area of parallelogram = 8 cm x 2.5 cm = 20 cm2

Example 2: 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:

(a) the area of the parallegram PQRS

(b) QN, if PS = 8 cm

Ans: Given:  SR=12 cm, QM = 7.6 cm, PS = 8cm

(a) Area of parallelogram = base x height = 12 x 7.6 = 91.2 cm2

(b) Area of parallelogram = base x height

=> 91.2 = 8 x QN => QN = 91.2/8 = 11.4 cm.

Question for Chapter Notes - Perimeter and Area
Try yourself:The area of the parallelogram ABCD in which AB = 6.2 cm and the perpendicular from C on AB is 5 cm is

## Area of Triangle

A triangle is a polygon with three vertices, and three sides or edges that are line segments. A triangle with vertices A, B, and C is denoted as ABC.Triangle ABC

To find the area of a triangle, you can follow these steps

• Identify the Triangle: Focus on one of the triangles within the parallelogram. The triangle's base is one side of the parallelogram, and the height is the perpendicular distance from the base to the opposite side.
• Understand the Relationship: Realize that the area of the parallelogram is twice the area of the triangle because the parallelogram can be divided into two congruent triangles.
• Calculate the area of Parallelogram :  Area=�×ℎArea= base x height.
• Apply the Relationship for the Triangle: Since the parallelogram is made up of two equal triangles, the area of one triangle is half the area of the parallelogram.

12×Are

Parallelogram ABCD

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

Example 1: Find BC, if the area of the triangle ABC is 36 cm2 and the height AD is 3 cm.
Ans: Height = 3 cm, Area = 36 cm2

Area of the triangle ABC = 1/2 x b x h
=> 36 = 1/2 x b x 3  => b = 24 cm
Base BC = 24 cm

Question for Chapter Notes - Perimeter and Area
Try yourself:Find the area of ∆ ABC

Example 2: Triangle ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC, is 6 cm. Find the area of Triangle ABC. What will be the height from C to AB i.e., CE?

Ans:  In triangle ABC, AD = 6cm and BC = 9cm
Area of triangle = 1/2 x base x height = 1/2 x AB x CE
=>  27 = 1/2 x 7.5 x CE
=>   CE = (27 x 2) /7.5  => CE = 7.2 cm
Height from C to AB ie.., CE is 7.2 cm

## Circles

A circle is defined as a collection of points on a plane that are at an equal distance.

Circle

Diameter: Any straight line segment that passes through the centre of a circle and whose end points are on the circle is called its diameter.

Radius: Any line segment from the centre of the circle to its circumference.

## Circumference of Circle

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

where,

• r is the radius of the circle
• π is an irrational number, whose value is approximately equal to 3.14

Circumference = Diameter x 3.14

Diameter(d) is equal to twice the radius(r) =2r

Circles with the same centre but different radii are called concentric circles.

Example: If the radius of the circle is 25 units, find the circumference of the circle. (Take π = 3.14)

Solution: Given, radius = 25 units

Let us write the circumference formula and then we will substitute the value of r (radius) in it.

Circumference of circle formula = 2πr

C = 2 × π × 25

C = 2 × 3.14 × 25 = 157 units

Therefore, the circumference of a circle is 157 units.

### Area of Circle

The area of a circle is the region enclosed in the circle.
Formulae of area of circle

where

• r is the radius of the circle
•  D is the diameter of the circle
• C is the circumference of the circle

Question for Chapter Notes - Perimeter and Area
Try yourself:What is the formula for the circumference of a circle?

Example 1: The radius of a circular pipe is 10 cm. What length of a tape is required to wrap once around the pipe (π = 3.14)?
Ans:
Radius of the pipe (r) = 10 cm
Length of tape required is equal to the circumference of the pipe. Circumference of the pipe = 2πr = 2 × 3.14 × 10 cm = 62.8 cm
Therefore, length of the tape needed to wrap once around the pipe is 62.8 cm.

Example 2: Find the perimeter of the given shape  (Take π = 22/7 ).

Ans: In this shape, we need to find the circumference of semicircles on each side of the square.Circumference of the circle = πd
Circumference of the semicircle = 1/2 πd = 1/2 x 22/7 × 14 cm = 22 cm Circumference of each of the semicircles is 22 cm

Therefore, the perimeter of the given figure = 4 × 22 cm = 88 cm.

Example 3: Diameter of a circular garden is 9.8 m. Find its area.
Ans:
Diameter, d = 9.8 m
Therefore, radius r = 9.8 ÷ 2 = 4.9 m
Area of the circle = πr2 = 22/7 x (4.9)2 m2 = 22/7 × 4.9 x 4.9 m2= 75.46 m2

Example 4:The adjoining figure shows two circles with the same centre. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm. Find:

(a) the area of the larger circle
(b) the area of the smaller circle
(c) the shaded area between the two circles. (π = 3.14)

Ans:
(a) Radius of the larger circle = 10 cm So, area of the larger circle = πr2 = 3.14 × 10 × 10 = 314 cm2
(b) Radius of the smaller circle = 4 cm Area of the smaller circle = πr2 = 3.14 × 4 × 4 = 50.24 cm2
(c) Area of the shaded region = (314 – 50.24) cm2 = 263.76 cm2

Question for Chapter Notes - Perimeter and Area
Try yourself:The area of a circle is 2464m2 , then the diameter is

The document Perimeter and Area Class 7 Notes Maths Chapter 9 is a part of the Class 7 Course Mathematics (Maths) Class 7.
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## Mathematics (Maths) Class 7

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## FAQs on Perimeter and Area Class 7 Notes Maths Chapter 9

 1. What is the formula to calculate the area of a parallelogram?
Ans. The formula to calculate the area of a parallelogram is base multiplied by height.
 2. How do you find the area of a triangle?
Ans. To find the area of a triangle, you can use the formula: Area = 1/2 * base * height.
 3. What is the formula to find the circumference of a circle?
Ans. The formula to find the circumference of a circle is C = 2πr, where r is the radius of the circle.
 4. How can you calculate the area of a circle?
Ans. The formula to calculate the area of a circle is A = πr^2, where r is the radius of the circle.
 5. How do you find the area of a parallelogram if the base and height are given?
Ans. To find the area of a parallelogram when the base and height are given, you can simply multiply the base by the height.

## Mathematics (Maths) Class 7

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