Key Points

The perimeter of a closed plane figure is the total distance covered along its boundary. For a polygon, it is simply the sum of the lengths of all its sides.

The perimeter of a rectangle is calculated using the formula: 2 multiplied by (length + breadth). This is because the opposite sides of a rectangle are equal in length.

The perimeter of a square is calculated by multiplying the length of one side by 4. The formula is: 4 multiplied by the length of a side, as all four sides are equal.

The perimeter of a triangle is the sum of the lengths of its three sides. For an equilateral triangle, where all sides are equal, the perimeter is 3 multiplied by the length of a side.

A regular polygon has all sides of equal length and all angles equal. The perimeter is found by multiplying the number of sides by the length of one side.

The area of a closed figure is the amount of region enclosed by its boundary. Area is measured in square units, such as square meters (sq m) or square centimeters (sq cm).

To find the area of a rectangle, you multiply its length by its breadth. The formula is Area = length x breadth.

The area of a square is found by multiplying the length of a side by itself. The formula is Area = side x side.

To find the area of complex shapes, you can split them into simpler figures like rectangles and squares. Calculate the area of each part and then add them together to find the total area.

The area of a triangle created by drawing a diagonal in a rectangle is exactly half the area of that rectangle. This principle helps in understanding the formula for the area of a triangle.

The area of an irregular shape can be estimated using a squared grid paper. You count the number of full squares, squares more than half-filled, and half-filled squares within the shape to find an approximate area.

It is important to remember that two shapes can have the same perimeter but different areas. Similarly, two shapes can have the same area but different perimeters.

Perimeter is used to solve problems like finding the length of fencing required for a park. Area is used for problems like finding the cost of tiling a floor or the number of trees that can be planted in a field.

If the area and one side of a rectangle are known, the other side can be found by dividing the area by the known side. If the perimeter and one side are known, the other side can be found using the perimeter formula.