 # Perimeter and Area Class 7 Notes: Chapter 11

### Perimeter

• Perimeter is the total length or total distance covered along the boundary of a closed shape. To know more about Perimeter, visit here.

### Area

• The area is the total amount of surface enclosed by a closed figure. ### The perimeter of Square and Rectangle

• Perimeter of a square = a + a + a + a = 4a, where a is the length of each side.
• Perimeter of a rectangle = l + l + b + b = 2(l + b), where l and b are length and breadth, respectively.

To know more about Perimeter Formula’s of All geometrical Figures, visit here.

### Area of Square & Rectangle

Area of square = 4a2

Here a is the length of each side

Area of rectangle = Length(l) × Breadth(b) = l×b

### Area of a Parallelogram • Area of parallelogram ABCD = (base×height)

Area of parallelogram ABCD  = (b×h)

### Triangle as Part of Rectangle

• The rectangle can be considered as a combination of two congruent triangles.
• Consider a rectangle ABCD, it is divided into 2 triangles ACD and ABD.
• Area of each triangle = 12 (Area of the rectangle).
12(10cm×5cm)
25cm2

### Area of a Triangle

• Consider a parallelogram ABCD.
• Draw a diagonal BD to divide the parallelogram into two congruent triangles.
• Area of triangle ABD = 1/2 (Area of parallelogram ABCD)

Area of triangle ABD  = 1/2 (b×h)

To know more about Area and Perimeter, visit here.

### Conversion of Units

• Kilometres, metres, centimetres, millimetres are units of length.
• 10 millimetres = 1 centimetre
• 100 centimetres = 1 metre
• 1000 metres = 1 kilometre

### Terms Related to Circle

• A circle is a simple closed curve which is not a polygon.
• A circle is a collection of points which are equidistant from a fixed point. • The fixed point in the middle is called the centre.
• The fixed distance is known as radius.
• The perimeter of a circle is also called as the circumference of the circle.

#### For More Information On Terms Related To Circle, Watch The Below Video. ### Circumference of a Circle

• The circumference of a circle ( C )  is the total path or total distance covered by the circle. It is also called a perimeter of the circle.

Circumference of a circle = 2×π×r,

where r is the radius of the circle.

## Visualizing Area of a Circle

### Area of Circle

• Area of a circle is the total region enclosed by the circle.

Area of a circle = π×r2, where r is the radius of the circle.

#### For More Information On Area Of Circle, Watch The Below Video. To know more about Circles, visit here.

### Introduction and Value of Pi

• Pi (π)  is the constant which is defined as the ratio of a circle’s circumference (2πr) to its diameter(2r).

π= Circumference (2πr)/Diameter (2r)

• The value of pi is approximately equal to 3.14159 or 22/7.

#### For More Information On The Value Of Pi, Watch The Below Video. To know more about Value of Pi, visit here.

## Problem Solving

### Cost of Framing, Fencing

• Cost of framing or fencing a land is calculated by finding its perimeter.
• Example: A square-shaped land has length of its side 10m.
Perimeter of the land = 4 × 10 = 40m
Cost of fencing 1m = Rs 10
Cost of fencing the land = 40 m × Rs 10 = Rs 400

### Cost of Painting, Laminating

• Cost of painting a surface depends on the area of the surface.
• Example: A wall has dimensions 5m×4m.
Area of the wall = 5m×4m=20m2
Cost of painting 1m2 of area is Rs 20.
Cost of painting the wall =20m2×Rs 20=Rs 400

### Area of Mixed Shapes

• Find the area of  the shaded portion using the given information.

Solution: Diameter of the semicircle = 10cm
Area of the shaded portion = Area of rectangle ABCD – Area of semicircle
Area of the shaded portion  = (l×b) − (πr2/2)
30×10 − (π×52/2)
= 300 − (π×25/2)
= (600 – 25π)/2
= (600 – 78.5)/2

= 260.7 cm2

#### 1 Comment

1. Tarak

Every useful
Thank you byjus
Love you