 # IMO Class 4 Chapter 7: Area and Perimeter of Geometrical Figures

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## IMO Class 4 Chapter 7: Area and Perimeter of Geometrical Figures Detailed Overview

The concepts of area and perimeter are crucial in understanding and analyzing various two-dimensional shapes in mathematics. Both area and perimeter are important concepts in real-life situations, such as measuring the area of a field or the perimeter of a fence. They are also crucial in many mathematical problems and applications, such as those encountered in engineering, physics, and architecture.

### What is Area?

Area is the amount of space occupied by a two-dimensional shape or object. Every shape has its own area, and it depends on its size and shape. For example, a square and a rectangle may have the same shape, but their areas are different because they have different sizes.

If we have two rectangular boxes with different lengths and widths, their areas will also be different. Only when both boxes have the same length and width will their areas be equal.

In simple terms, the area of a shape is like the space inside it. It depends on the size and shape of the shape, and different shapes have different areas. Even if two shapes have the same shape, their areas will be different if their sizes are different. To have the same area, two shapes need to have the same size and shape.

### What is Perimeter?

The perimeter of a shape is the total distance around its edges. It is like the length of a shape if you were to stretch it out in a straight line. The perimeter of a two-dimensional shape is the complete length of its boundary.

Different shapes can have the same perimeter even if they have different measurements. For example, a circle made of a metal wire with a length of L can also be used to make a square with sides of the same length. This is because the circumference of a circle and the perimeter of a square can be the same, even though the shapes are different.

### Area and Perimeter For all Shapes

Area and perimeter can be calculated for different shapes like squares, rectangles, circles, triangles, and many others.

### Area and Perimeter of a Rectangle

The area of a rectangle can be found by multiplying its length by its width. The perimeter of a rectangle is the sum of the lengths of all its sides.

A rectangle’s perimeter equals = 2(a + b).

Rectangle Area = a x  b

### Perimeter and Area of a Square

The area of a square can be found by multiplying its length by its width. The perimeter of a square is the sum of the lengths of all its sides.

The perimeter of a Square = 4a

Area of a Square = a2

### Perimeter and Area of Triangle

The area of a triangle can be found by multiplying the length of its base by its height, and then dividing the result by 2. The perimeter of a triangle is the sum of the lengths of all its sides.

The perimeter of a triangle = a + b +c, where a, b and c are the three different sides of the triangle.

Area of a triangle = ½ x b × h; where b is the base and h is the height of the triangle.

### Area and Circumference of a circle

The area of a circle can be found by multiplying the radius of the circle squared by the value of pi (π). The perimeter of a circle is known as its circumference, which can be found by multiplying the diameter of the circle by the value of pi (π).

Circumference of Circle = 2πr

Area of Circle = πr2

### Applications of Area and perimeter

Area is the amount of space inside a shape, and perimeter is the distance around the outside of a shape. These concepts are used in many real-life situations, such as:

1. Fencing a garden or a field: The perimeter of the area to be fenced needs to be measured to determine the amount of fencing material required.
2. Carpeting a room: The area of the room needs to be measured to determine how much carpet will be required to cover the floor.
3. Painting a wall: The area of the wall needs to be measured to determine how much paint will be required to cover the wall.
4. Buying tiles for a bathroom: The area of the bathroom floor needs to be measured to determine the number of tiles required to cover the floor.
5. Planning a playground: The perimeter of the playground needs to be measured to determine the length of fencing required, and the area needs to be measured to determine the amount of ground surface area available for activities.

So, area and perimeter are important concepts that help us determine the size, amount, and quantity of things we need for many real-life situations.

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