Maharashtra Board Class 7 Maths part 2 Chapter 12 Perimeter and Area PDF Download

Perimeter And Area

Let's Recall

Perimeter

The sum of the lengths of all sides of a closed figure is the perimeter of that figure.

Perimeter of a polygon = sum of lengths of all sides.

Perimeter of a square = 4 × side

Perimeter of a rectangle = 2 length + 2 breadth

Perimeter of square of side a = 4a

Perimeter of a rectangle with length l and breadth b is 2l + 2b

Example

The perimeter of a rectangle is 64 cm. If its length is 17 cm, what is its breadth?

Solution

Let its breadth be x cm.

2 length + 2 breadth = perimeter

2 (length + breadth) = 64

2 (17 + x) = 64

\[\frac{2(17 + x)}{2} = \frac{64}{2}\]

17 + x = 32

x = 15

The breadth of the rectangle is 15 cm.

Example

The perimeter of a rectangle of length 28 cm and breadth 20 cm is equal to the perimeter of a square. What is the length of the side of that square?

Solution

Perimeter of rectangle = 2 (length + breadth)

= 2 (28 + 20)

= 96

If the side of that square is a then 4a = 96

Perimeter of square = 96

4a = 96

\[\therefore a = \frac{96}{4} = 24\]

Side of the square is 24 cm.

Teacher's Note

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

Exam Trick

Remember: For a rectangle, perimeter = 2 (length + breadth). For a square, perimeter = 4 × side. Always use these formulas in exams.

Points to Remember

Perimeter is the distance around a closed shape.
For a rectangle, add all four sides: 2l + 2b.
For a square, multiply side by 4: 4a.
Perimeter is measured in cm, m, or km.

Practice Set 44

1. If the length and breadth of a rectangle are doubled, how many times the perimeter of the old rectangle will that of the new rectangle be?

2. If the side of a square is tripled, how many times the perimeter of the first square will that of the new square be?

3. Given alongside is the diagram of a playground. It shows the length of its sides. Find the perimeter of the playground.

4. As shown in the figure, four napkins all of the same size were made from a square piece of cloth of length 1 m. What length of lace will be required to trim all four sides of all the napkins?

Area

Area of square = side × side = (side)²

Area of rectangle = length × breadth = l × b

Area is measured in square metres, square cm, square km, etc.

Activity I

Measure the length and breadth of the courts laid out for games such as kho-kho, kabaddi, tennis, badminton, etc. Find out their perimeters and areas.

Activity II

A wall in Aniruddha's house is to be painted. The wall is 7 m long and 5 m high. If the painter charges 120 rupees per square metre, how much will he have to be paid?

Example

A rectangular garden is 40 m long and 30 m wide. A two-metre wide path is to be paved inside the garden along its boundary, using tiles 25 cm × 20 cm in size. How many such tiles will be required?

Solution

Let us find the area to be paved.

Area of garden = 40 × 30 = 1200 sqm

Area not to be paved = 36 × 26 = 936 sqm

\[\therefore\] Area to be paved = 1200 - 936 = 264 sqm

Area of each tile = \[\frac{25}{100} \times \frac{20}{100} = \frac{1}{20}\] sqm

Area of one tile is \[\frac{1}{20}\] sqm.

Hence, let us find the number of tiles required to tile 264 sqm.

Number of tiles = \[\frac{\text{Total area}}{\text{Area of one paver}}\]

= \[264 \div \frac{1}{20}\]

= 264 × 20 = 5280

Therefore, 5280 tiles will be required.

Teacher's Note

Area tells us how much space something covers. When you paint a wall in your house, you need to know its area to buy the right amount of paint.

Exam Trick

Remember: Area of rectangle = length × breadth. Area of square = side × side. Always write units as square cm or square m in your answer.

Points to Remember

Area is the space inside a shape.
For a rectangle, multiply length and breadth.
For a square, multiply side by itself.
Area is measured in square units like cm² or m².

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