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# Area and Perimeter

Every polygon will have a specific area and perimeter. We need the area to find the quantity stored inside a shape or the space that a shape can hold. Whereas we need to find the perimeter to know how much space the complete polygon needs to fit in a particular region. The area is the space bounded inside a closed polygon. The amount of space occupied by a shape is its area. For example, the space in a blackboard where the teacher writes is an area. The units of the area are square. Perimeter is the outer periphery of any shape. It is the sum of all the sides of a shape. For example, we need to find the perimeter of soccer to know how much space it will take to be kept on a table. The units of the perimeter are the same as that of the side of the polygon.

## Difference between area and perimeter

 Area Perimeter It is the space bounded inside a shape or object. It is the total length of all the sides of a polygon. The inner space is not included, only the boundary of a polygon is taken into consideration. It is measured in square units. The units may change as per the dimensions of the shape whose area we need to find, like centimetre, inches, feet, etc. The units are the same as the length of the side of the polygon. For example, the area of a rectangle is equal to the product of its length and breadth. For example, the perimeter of a circle is the outer boundary of a circle given by 2 x π x radius of the circle.

## Area and perimeter formula for different shapes

 Shape Area (square units) Perimeter (units) Square side × side 4 × side Rectangle length × width 2(length + width) Circle 2πr πr² Equilateral Triangle side + side + side (1/2) × base × height Parallelogram 2 × (sum of two parallel sides) base × height Rhombus 4 × side (1/2) × diagonal 1 × diagonal 2

Example 1: What is the perimeter of a square playground whose each side length is 11 cm?

Solution:

We know the perimeter of any shape is equal to the sum of its sides. Also, a square is a four-sided figure whose all sides are equal. Therefore, Perimeter of square = sum of its sides = 4 x length of each side = 4 × 12 cm

Example 2: The sides of a polygon are given by 6 cm, 8 cm, 10 cm, 2 cm, and 15 cm. Find the perimeter.

Solution:

We know the sum of sides of any polygon is equal to its perimeter. Therefore, the perimeter of the given polygon is 6 + 8 + 10 + 2 + 15 = 41 cm.

Example 3: Find the area of a trapezium whose length of parallel sides is equal to 8 cm and height is 10 cm.

Solution:

We know the area of trapezium is given by: ½ x base x height Therefore, the area = ½ x 8 x 10 = 40 cm².

Example 4: Find the inner area of a square park whose outer side is 100 m and inner side is 50 m.

Solution:

The outer side of the park is 100 m. Therefore,
The area of the park = 100 x 100 = 10,000 m²
The inner side of the part is equal to 50 m. Therefore,
The area of park = 50 x 50 = 2500 m²
The final area of the park is equal to the difference of the outside park area and inner park area. Therefore,
The area of the inner park = 10,000 – 2500 = 7500 m².

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