# Chapter 11 – Perimeter and Area

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

We see various objects and shapes in our daily lives. These shapes are formed when lines are joined together as boundaries. The area interior to these shapes defines the perimeter and area of the shapes. Learning about the perimeter and area of different shapes helps us figure out the space taken by a particular figure. Here, we will learn about a perimeter and area and the formulas to calculate the areas and perimeter of different shapes.

#### Perimeter and Area

The perimeter can be understood as a path that covers a two-dimensional figure or shape. It is the length of the shape such as a triangle, square, rectangle etc. It is the length of the outline of a particular shape. Perimeter enables us to determine the length of a figure, and its measures are centimetres (cm) or metres (m).

The area is defined as the space occupied by a flat object or a shape. The area is the number of unit squares covered by the flat object or by the surface of any other shape. It determines the area which touches the surface and is measured as a square metre. It is measured in square inches, square feet, and square centimetres.

#### Squares and Rectangles

A square is a two-dimensional figure or a shape with four equal sides. It is a quadrilateral that has four sides and fours vertices.

Perimeter of a Square
The perimeter of a square is the sum of all four sides.

• Perimeter of a square = a + a + a + a = 4a, where, a is the length of each side.

Area of a Square
The area of a square is two times the side.

• Area of a square = Side*Side square unit, where the side is the length of each side.

A rectangle is a quadrilateral figure where every angle is a right angle or at 90 degrees. It has four sides with all the opposite sides equal and parallel in length.

Perimeter of a Rectangle
The perimeter of a rectangle is two times the length and breadth of the rectangle.

• The perimeter of a rectangle = 2(L+B), where L is length, and B is the breadth of the rectangle.

Area of a Rectangle
The area of the rectangle is multiple of the length and breadth of the rectangle.

• Area of a rectangle = L*W, where L is length, and W is the width of the rectangle.

#### Triangles as Parts of Rectangles

A rectangle can be imagined as a figure which is made of two congruent triangles. These triangles are equal in area.

• The area of each triangle = 1/2 (Area of the rectangle)
• The area of each triangle = 1/4 (Area of the square)

#### Area of Parallelogram

A parallelogram is a figure where two opposite sides are equal in length and are parallel to each other. All the interior angles in a parallelogram are equal in measures.

• Area of a parallelogram= B*H, where B is the base, and H is the height of the parallelogram.

For the base of the parallelogram, any side can be taken, and the height is the side from which a perpendicular is dropped on the base from any opposite vertice.

#### Area of Triangle

Area of a Triangle can be measured through a parallelogram. As the area of a triangle is half of the area of a parallelogram. We can calculate the area of a triangle by constructing a diagonal intersection in the parallelogram. This enables us to identify the height and base of the triangle.

• Area of a triangle= ½ (B*H), where B is the base, and H is the height of the triangle.

#### Area of Circle

A circle is a closed round figure which is based on different points. It is a collection of different points that are equidistant from a central point. For a circle, the fixed point, which is equidistant, is known as the centre, and the fixed distance is known as the radius of the circle.

• The perimeter of a circle= 2×π×r, where r is the radius of the circle, and π is the value 22/7.
• The perimeter of a circle is also known as the circumference of the circle.
• Area of a circle = π×r2, where r is the radius of the circle and π is the value 22/7.

Area of a circle is the total region covered by the circle. The circumference of a circle is the total distance or path that is covered by a circle.

#### Conversion of Units

• Kilometres, metres, centimetres, millimetres are units of length.
• 10 millimetres = 1 centimetre
• 100 centimetres = 1 metre
• 1000 metres = 1 kilometre
• 1 cm2 = 100 mm2
• 1 m2 = 10000 cm2
• 1 hectare = 10000 m2

#### FAQs

1. What is the formula for perimeter and area?
Area of a square = Side*SidePerimeter of a square = a + a + a + a = 4a
2. What is perimeter and area with examples?
A square with sides of 2cm will have a perimeter and area as follows:
Perimeter= a + a + a + a = 4aP= 4*2
P= 8 square unit
Area= Side*Side
A= 2*2
A= 4 square unit
3. How do you find the area? What is the formula perimeter?
Area of a rectangle = L*W, where L is length, and W is the width of the rectangle.
Perimeter of a rectangle = 2(L+B), where L is length, and B is the breadth of the rectangle.
4. What is the area and perimeter of the square?
Area of a square = Side*SidePerimeter of a square = a + a + a + a = 4a

To learn more about perimeters and areas of other shapes and figures, download the MSVgo application on iOS App Store, Google Play Store or visit the website. It is a fun video library application where you can learn with examples, explanatory visualisations and animations, along with interactive learning methods.

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