Solution of Try These NCERT Exercise 11.1

Perimeter and Area 7th Math

Solution of Try These NCERT Exercise 11.1

Important Formulas relating to Area and perimeter of rectangle and square

Area of Rectangle = Length × Breadth

Length of rectangle = Area of Rectangle/Breadth

Breadth of rectangle = Area of Rectangle/Length

Area of Square = Side2

Side of square = Area of square

Perimeter of Rectangle = 2 (Length + Breadth)

Length of rectangle = Perimeter of Rectangle/2 – Breadth

Breadth of rectangle = Perimeter of Rectangle/2 – Length

Perimeter of Square = 4 × side

Side = Perimeter of square/4

Solution of Try These (11.1) [NCERT Book-math class 7]

What would you need to find, area or perimeter to answer the following?

Question (1) How much space does a blackboard occupy?

Answer: Area

Question (2) What is the length of a wire require to fence a rectangular flower bed?

Answer: Perimeter.

Question (3) What distance would you cover by taking two rounds of a triangular park?

Answer: Perimetre

Question (4) How much plastic sheet do you need to cover a rectangular swimming pool?

Answer: Area of swimming pool.

Solution of Try These (11.2) [NCERT Book]

Question (1) Experiment with several such shapes and cut–outs. You might find it useful to draw these shapes on squared sheets and computer their areas and perimeter.

Answer Do it yourself.

You have seen that increase in perimeter does not mean that area will also increase.

Question (2) Give two examples where the area increases as the perimeter increases.

Answer When length or width of a rectangle increases, the area and perimeter both increases.

Example (i)

Let ABCD is a rectangle.

class 7th math Perimeter and area question1 try these

In which AB = length = 5 m. And width BC = 3 m

We know that,

Area of a rectangle = Length × Breadth

= 5 m × 3 m

= 15 m2

Thus, area of the given rectangle = 15 m2

And, Again we know that

Perimeter of a rectangle = 2(Length + Breadth)

= 2( 5m + 3 m)

= 2 × 8 m

= 16 m

Thus, Perimeter of the given rectangle = 16 m

class 7th math Perimeter and area question2 try these

Now, Let, Length of the Rectangle increases from 5 m to 7 m

Thus, now new length = 7 m

And breadth (as previous) = 3 m

Now,

We know that, Area of a rectangle = Length × Breadth

= 7 m × 3 m

= 21 m2

Thus, Area of rectangle after increase in length = 21 m2

Now, We know that, perimeter of the rectangle = 2(Length + Breadth)

= 2(7 m + 3 m)

= 2 × 10 m = 20 m

Thus, perimeter of the rectangle after increase in length = 20 m

Now, if is clear that, area increase as perimeter increases.

Example (ii)

Let ABCD is a square, in which side is equal to 5 cm

class 7th math Perimeter and area question2 example try these

Now, we know that,

Perimeter of a square = 4 × side

= 4 × 5 cm

= 20 cm

Thus, perimeter of the square = 20 cm

Now, We know that,

Area of a square = side2

Thus, area of the square = (20 cm)2

= 400 cm2

Thus, area of the square = 400 cm2

Now, when, side increase with 2 cm, i.e. increases from 5 cm to 5+2 = 7 cm

class 7th math Perimeter and area question2 example_2 try these

Then, Perimeter of the square = 4 × side

= 4 × 7 cm

= 28 cm

Thus, perimeter of the square = 28 cm

Now, Area of the square = side2

= (7 cm)2

= 49 cm2

Thus, area of the square = 49 cm2

Now, it is clear that, when the perimeter increases, the area also increases.

Question (3) Give two examples where the area does not increase when the perimeter increases.

Answer:

Example (i) Area does not increase when perimeter increases

class 7th math Perimeter and area question3 example_1 try these

Let, ABCD is a rectangle having length (AB) = 5 cm

And width (BD)= 3 cm

Now, the Area of the rectangle = Length × Breadth

= 5 cm × 3 cm

= 15 cm2

Or, the Area of the rectangle = 15 cm2

Now, Perimeter of the rectangle = 2(Length + Breadth)

= 2 (5 cm + 3 cm)

= 2 × 8 cm

Thus, the Perimeter of the rectangle = 16 cm

Now, Let, a square side of 1cm is cut from AB

class 7th math Perimeter and area question3 example_1a try these

Now the length of the upper side of the rectangle

= (AB – 1 cm) + FG + HG + HB

= (5 cm – 1 cm) + 1 cm + 1 cm + 1 cm

= 4 cm + 3 cm

= 7 cm

And, AC = 3 cm, BD = 3 cm, CD = 5 cm

Thus, the Perimeter of the given rectangle

= Length of upper side + AC + BD + CD

= 7 cm + 3 cm + 3 cm + 5 cm

= 18 cm

Thus, the perimeter of the rectangle after cutting out a square of 1 cm = 18 cm

Now, Area of the rectangle without cutting out of the square = 15 cm2

{As calculated above}

And area of square cut out = side2

= (1 cm)2

= 1 cm2

Thus, Area of rectangle without square

= Area of rectangle without cutting out of square – area of square

= 15 cm2 – 1 cm2

= 14 cm2

Thus, area of square without square = 14 cm2

And perimeter of the square without square = 18 cm

Thus, here it becomes clear that, in the case of an increase in perimeter, the area does not increase.

Example (2) Area does not increase when perimeter increases

class 7th math Perimeter and area question3 example_1b try these

Here, Area of the rectangle = 14 cm2

And Perimeter of the rectangle = 18 cm

Let, another square MNOP cut out from the CD side of the rectangle.

class 7th math Perimeter and area question3 example_1c try these

Now, New perimeter of the rectangle

= [(AB – EH) + EF + FG + HG] + AC + BD + [(CD Ó MN) + MP + PO + ON]

= [(5cm – 1cm) + 1cm + 1cm + 1cm] + 3cm + 3cm [(5cm – 1cm) + 1cm + 1cm + 1cm]

= 7 cm + 6 cm + 7cm

= 21 cm

And the new area of the rectangle after cutting out of the second square

= Area of rectangle without one square – Area of second square

= 14 cm2 – 1 cm2

= 13 cm2

Thus, here it becomes clear that, in the case of an increase in perimeter, the area does not increase.

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