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Maths > Mensuration > Area and Perimeter
Mensuration

Area and Perimeter

If you want to fence a plot, how would you calculate how much fencing is required? Or if your parents want to put a new carpet in your room, how much carpet you need to buy? Clueless about the concepts of Area and Perimeter? Let us study them in detail.

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Area and Perimeter

Area and Perimeter are very important terms while dealing with mathematics. This applies to any shape of the field, irregular or regular. The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence. If the yard is 50 ft ×  50 ft your fence is 200 ft long.

The area is a measure of the space contained within an object. In the same yard, an area is a measure you need to be to start a lawn. The area has units of distance squared. For a 50 ft × 50 ft you need 50 × 50 = 2500 sq feet of grass. So let us find out the Area and Perimeter of the figures given below.

Area and Perimeter

What is Area?

The area is the amount of two-dimensional space taken up by the object. It is measured in square units.

Formulas for Finding Area

  • Area of the rectangle =  length × width
  • Area of the Square = s², where ‘s’ = sides of the square
  • The area of a triangle is A = \( \frac{1}{2} \) b × h  where’ b’ is the base and ‘ h’ is the height
  • Area of the circle = πr² where ‘ r ‘ is the radius
  • The area of the parallelogram is A = b × h; here b = base and h =vertical height
  • Area of parallelogram = base × height
  • Area of rhombus = base × height
  • The Area of trapezium = 1/2 (sum of parallel sides) × (perpendicular distance between them)

What is Perimeter?

A perimeter is the total boundary of the two-dimensional shape. If you want to provide a fencing around the entire field you need its perimeter. Suppose you want to lay a pathway inside the field to keep a watch on your field you need its perimeter. The units of the perimeter are, cm, m etc.

Formulas for Finding Perimeter

  • Perimeter of Rectangle: We can see that in the rectangle the two sides are parallel and equal and also all the angles are 90 degrees. P = l+ b+ l+ b = 2l + 2b = 2 ( l + b )
Area and Perimeter
  • Perimeter of Square: So a rectangle with all its sides equal is a square. A perimeter of a square is 4 × S
  • The Perimeter of a Triangle: is given by P = (a + b + c), where a, b and c are the 3 sides of the triangle.
  • Perimeter of Parallelogram = 2 (sum of adjacent sides)
  • Perimeter of Rhombus = 4 × side

Solved Examples For You

Question 1: The perimeter of the rectangle whose length = 25 cm and breadth = 15 cm is ……….cm

  1. 40
  2. 80
  3. 50
  4. 81

Answer: B. The perimeter of a rectangle = 2 × ( length + breadth )
Hence perimeter = 2 × ( 25 + 15  ) = 80cm

Question 2: A square garden 10 feet long needs to be surrounded by a walk of 2 feet wide on only three of its sides. What is the area of the walk?

  1. 55 sq.ft
  2. 58 sq.ft
  3. 68 sq.ft
  4. 70 sq.ft

Answer: C. The total area of the garden = side²
Therefore total area = 10² = 100
If we consider the walkway of rectangles with dimensions  12 and 14 respectively,
Area = l × b
The total area of the walk = Total area – total area of the garden
= 168 – 100 = 68 sq. ft

Question 2: What is the perimeter?

Answer: A perimeter refers to the total boundary of the two-dimensional shape. If we want to offer fencing around the whole field, we will need its perimeter. If we wish to lay a trail inside the field to keep a watch on the field, we will need its perimeter. Similarly, the units of the perimeter are, cm, m etc.

Question 3: How do you find the area?

Answer: To find the area of a rectangle, you need to multiply its height by its width. For a square, we just need to find the length of one of the sides. Remember, each side is the same length. Then, we will multiply this by itself to find out the area.

Question 4: What is the difference between area and perimeter?

Answer: Area simply means, the ‘space covered’, in other words, inside of the objects. Whereas perimeter refers to the distance around, this is the outline of the shape. In addition, figures having the same perimeter can have a different area. On the other hand, figures having the same area can have a different perimeter.

Question 5: What shape gives the most area?

Answer: A circle is a shape that consists of the largest area of any two-dimensional object that has the same perimeter. A cyclic polygon which is inscribed in a circle consists of the largest area of any polygon with a given number of sides of the same lengths.

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