Maharashtra Board Class 5 Maths Part Two Chapter 12 Perimeter and Area PDF Download

12. Perimeter And Area

Perimeter: Revision

Closed figures have a perimeter. You know that the sum of the lengths of all the sides of a figure is called its perimeter.

Fill in the empty boxes in the following problems.

1. The lengths of the adjacent sides of rectangle ABCD are given. The perimeter of rectangle ABCD is ___ cm. Remember, the lengths of the opposite sides of a rectangle are equal.

2. The length of the adjacent sides of a rectangle are 10 cm and 7 cm. The perimeter of the rectangle is ___ cm.

3. The length of a side of square PQRS is 5 cm. The perimeter of square PQRS is ___ cm.

4. In triangle ABC, the length of side AB is 4 cm, the length of BC is 8 cm and the length of CA is 6 cm. The perimeter of triangle ABC is ___ cm.

Problem Set 48

1. Write the perimeter of each figure in the box given below it.

Teacher's Note

Perimeter means the distance around a shape. When you walk around your school playground, you are walking the perimeter.

Exam Trick

Remember: Perimeter = add all sides. Just count how many sides the shape has and add each one.

Points To Remember

Perimeter is the distance around a closed shape.
We add all the side lengths to find perimeter.
Rectangle has opposite sides equal.
Square has all sides equal.
Perimeter units are cm or m, not sq cm.

Formula For The Perimeter Of A Rectangle

Perimeter = length + breadth + length + breadth

Opposite sides of a rectangle are of the same length. So, the perimeter of a rectangle = twice the length + twice the breadth = 2 × length + 2 × breadth

Perimeter of a rectangle = 2 × length + 2 × breadth

Example: The length of the rectangle below is 7 cm and its breadth, 3 cm. Let us find its perimeter.

Perimeter of rectangle PQRS = 2 × length + 2 × breadth = 2 × 7 + 2 × 3 = 14 + 6 = 20

Therefore, the perimeter of the rectangle is 20 cm.

Formula For The Perimeter Of A Square

The lengths of all the sides of a square are equal. Therefore, the perimeter of a square = four times the length of one of its sides.

Perimeter of a square = 4 × the length of one side

Example: The length of one side of a square is 6 cm. Find its perimeter.

The perimeter of a square is four times the length of one side.

Perimeter of a square = 4 × length of one side = 4 × 6 = 24

Therefore, the perimeter of the square is 24 cm.

Teacher's Note

For rectangles and squares, we use formulas to find perimeter quickly. If your classroom is 10 m long and 8 m wide, the perimeter is 2(10) + 2(8) = 36 m.

Exam Trick

Rectangle perimeter formula: 2(L + B). For square: just multiply one side by 4. This is much faster than counting!

Points To Remember

Rectangle perimeter = 2 × length + 2 × breadth.
Square perimeter = 4 × one side.
Both formulas save time.
Always write the unit (cm or m).
Opposite sides of rectangle are equal.

Word Problems

Example (1) The length of a rectangular park is 100 m, while its width is 80 m. What is its perimeter?

Perimeter of the rectangle = 2 × length + 2 × breadth = 2 × 100 + 2 × 80 = 200 + 160 = 360

The perimeter of the rectangular park is 360 m.

Example (2) How much wire will be needed to put a triple fence around a square plot with side 30 m? What will be the total cost of the wire at ₹ 70 per metre?

To put a single fence around the square plot, we need to find its perimeter.

Perimeter of a square = 4 × length of one side = 4 × 30 = 120

The perimeter of the square plot is 120 metres. Since the fence is to be a triple fence, we must triple the perimeter.

120 × 3 = 360 m of wire will be needed.

Now let us find out how much the wire will cost. One metre of wire costs ₹ 70. Therefore, the cost of 360 m of wire will be 360 × 70 = 25,200.

The total cost of wire for putting a triple fence around the plot will be ₹ 25,200.

Problem Set 49

1. How much wire will be needed to make a rectangle 7 cm long and 4 cm wide?

2. If the length of a rectangle is 20m and its width is 12m, what is its perimeter?

3. Each side of a square is 9m long. Find its perimeter.

4. If we take 4 rounds around a field that is 160 m long and 90 m wide, what is the distance we walk in kilometres?

5. Sanju completes 12 rounds around a square park every day. If one side of the park is 120 m, find out in kilometres and metres the distance that Sanju covers daily.

6. The length of a rectangular plot of land is 50 m and its width is 30 m. A triple fence has to be put along its edges. If the wire costs 60 rupees per metre, what will be the total cost of the wire needed for the fence?

7. A game requires its players to run around a square playground. Each side of the playground is 20 m long. One player took 5 rounds around the playground. How many metres did he run altogether?

8. Four rounds of wire fence have to be put around a field. If the field is 60 m long and 40 m wide, how much wire will be needed?

9. The sides of a triangle are 24.7cm, 20.4 cm and 10.5 cm respectively. What is the perimeter of the triangle?

Teacher's Note

Word problems help us use perimeter in real life. In India, farmers often fence their fields. They need to know how much wire to buy.

Exam Trick

For triple or multiple fences, find the perimeter first, then multiply by the number of rounds. This makes it easy!

Points To Remember

Always find perimeter first before solving word problems.
Multiply perimeter by the number of rounds.
Convert metres to kilometres if needed (1 km = 1000 m).
Read the question carefully for what is asked.
Check your answer with the units.

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