Q.1 The length and the breadth of a rectangular piece of land are 500 m and 300 m respectively. Find

(i) its area

(ii) the cost of the land, if 1\( m^2 \) of the land costs Rs. 10,000

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: l = 500 m, b = 300 m

(i) Area = l × b

= 500 m × 300 m = 150000\( m^2 \)

(ii)
\(\because \)Cost of 1\( m^2\) land = Rs.10,000

\(\therefore \)cost of 150000\( m^2 \) land = Rs. 10,000×1,50,000= Rs.15,00,000,000

Q.3Find the breadth of a rectangular plot of land, if its area is 440\( m^2 \)and the length is 22 m. Also, find its perimeter.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Area = 440\( m^2\)

Length = 22 m

Breadth = \(\frac{Area}{Length} =\frac{440m^2}{22m}=20m \)

Breadth = 20 m

Perimeter = 2(l + b) = 2 (22 m + 20 m)

= 2 × 42 m = 84 m

Q.4 The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Perimeter = 100 cm

Length = 35 cm

Perimeter = 2(l + b)

100 = 2(35 + b)

Or, \(\frac{100}{2}= 35+b \)

Or, b= 50 - 35 = 15 cm

Area = l×b = 35cm × 15 cm =\( 525 cm^2 \)

Q. 5 The area of a square park is same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Side of the square park = 60 m

Length of the rectangular park = 90 m

Area of the rectangular park = Area of the square park

Or, l×b = side × side

Or, 90× b = 60×60

Or, b = \(\frac{60×60}{90} \) = 40m

Hence, the required breadth = 40 m.

Q.6 A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Length = 40 cm,

Breadth = 22 cm

Perimeter of the rectangle= Length of the wire

= 2(l + b) = 2(40 cm + 22 cm)

= 2 × 62 cm = 124 cm

Now, the wire is rebent into a square.

Perimeter = 124 cm

Or, 4 × side = 124

\(\therefore \)side = \(\frac{124}{4} \) cm = 31 cm

So, the measure of each side = 31 cm

Area of rectangular shape = l × b

= 40 cm x 22 cm = 880\( cm^2\)

Area of square shape = Side× side

= \( (31)^2 = 961 cm^2 \)

Since 961\( cm^2 > 880 cm^2 \)

Hence, the square encloses more area.

Q.7 The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also find the area of the rectangle.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Perimeter = 130 cm

Breadth = 30 cm

Perimeter = 2 (l + b)

130 cm = 2(l + 30 cm)

Or, \(\frac{130}{2} \)cm = l + 30 cm

Or, 65 cm = l + 30 cm

Or, 65 cm – 30 cm = l

\(\therefore \)l = 35 cm

Area of the rectangle = l × b = 35 cm × 30 cm

= 1050 \(cm^2\)

Q.8 A door of length 2 m and breadth 1 m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m (Fig). Find the cost of white washing the wall, if the rate of white washing the wall is ? 20 per\(m^2.\)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Length of wall = 4.5 m

Breadth of the wall = 3.6 m

Length of the door = 2 m

Breadth of the door = 1 m

Area of the wall = l × b = 4.5 m × 3.6 m = 16.20\( m^2 \)

Area of the door = l × b = 2 m × 1 m = 2 \(m^2\)

\(\therefore \) Area of the wall to be white washed = Area of the wall – Area of the door

= 16.20 \(m^2 – 2 m^2= 14.20 m^2\)

Cost of white washing

= Rs. 14.20 × 20 = Rs. 284.00

Hence, the required area = 14.20\( m^2 \)and the required cost = Rs. 284

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

(a) Area of the parallelogram

= base × altitude = 7 cm × 4 cm

= 28 \( cm^2\)

(b) Area of the parallelogram

= base × altitude = 5 cm × 3 cm

= 15\( cm^2\)

(c) Area of the parallelogram

= base × altitude = 2.5 cm × 3.5 cm

= 8.75\( cm^2 \)

(d) Area of the parallelogram

= base × altitude = 5 cm × 4.8 cm

= 24.0 \( cm^2 \)

(e) Area of the parallelogram

= base × altitude = 2 cm × 4.4 cm

= 8.8 \( cm^2\)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Area of the triangle =\(\frac{1}{2} \) × b × h

= \(\frac{1}{2} \) × 4 cm × 3 cm

=\( 6m^2\)

(b) Area of the triangle = \(\frac{1}{2} \) × b × h

= \(\frac{1}{2} \) × 5 cm × 3.2 cm

= 8.0\( cm^2\)

(c) Area of the triangle = \(\frac{1}{2} \) × b × l

= \(\frac{1}{2} \) × 3 cm × 4 cm

= 6\( cm^2 \)

(d) Area of the triangle = \(\frac{1}{2} \) × b × h

= \(\frac{1}{2} \) × 3 cm × 2 cm

= 3 \(cm^2\)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

(a) Area of the parallelogram =b × h

Or, b×h =\( 246 cm^2 \)

Or, 20 cm × h =\( 246 cm^2\)

Or, h = \( 246cm^2\) /20 cm = 12.3 cm

(b) Area of the parallelogram =b × h

Or, b×h =\( 246 cm^2 \)

Or, b × 15 cm =\( 154.5 cm^2\)

Or, b = \( 154.5 cm^2\) /15 cm = 10.3 cm

(c) Area of the parallelogram =b × h

Or, b×h =\( 48.72 cm^2 \)

Or, 8.4 cm × h =\( 48.72 cm^2\)

Or, h = \( 48.72cm^2\) /8.4 cm = 5.8 cm

(d) Area of the parallelogram =b × h

Or, b×h =\( 16.38 cm^2 \)

Or, b × 15.6 cm =\( 16.38 cm^2\)

Or, b = \( 16.38 cm^2\) /15.6 cm = 1.05 cm

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

(i) Area of the triangle = \(\frac{1}{2} \)× b × h

\(87cm^2 \) = \(\frac{1}{2} \) × 15 × h

Or, h = \(\frac{87×2}{15} \) = \(\frac{174}{15} \) = 11.6cm

(ii) Area of the triangle = \(\frac{1}{2} \)× b × h

\(1256cm^2 \) = \(\frac{1}{2} \) × b × 31.4

Or, b = \(\frac{1256×2}{31.4} \) = 40×2 = 80 mm

(iii) Area of the triangle = \(\frac{1}{2} \)× b × h

\(170.5cm^2 \) = \(\frac{1}{2} \) × 22 × h

Or, h = \(\frac{170.5×2}{22} \) = 15.5 cm

Q.5 PQRS is a parallelogram. QM is the height of Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find:

(a) the area of the parallelogram PQRS

(b) QN, if PS = 8 cm

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

(a) Area of the parallelogram PQRS = Base × Height

= SR × QM

= 12 cm × 7.6 cm

= 91.2 \( cm^2 \)

(b) Area of the parallelogram PQRS = Base × Height

Or, 91.2 = PS×QN

Or, 91.2 = 8× QN

Or, QN = 91.2 / 8 = 11.4 cm

Q.6 DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is 1470\( cm^2 \), AB = 35 cm and AD = 49 cm, find the length of BM and DL.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Area of the parallelogram ABCD = base × height

= AB × DL= 1470 \(cm^ 2 \)

Or, 35 cm × DL = 1470 \(cm^ 2 \)

Or, DL= 1470/ 35

\(\therefore \) DL = 42 cm

Area of the parallelogram ABCD = AD × BM

1470 \( cm^2 \) = 49 cm × BM

Or, 1470/ 49 = BM

\(\therefore \) BM = 30 cm

Hence, BM = 30 cm and DL = 42 cm

Q.7 \(\triangle \) ABC is right angled at A. AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, find the area of\(\triangle \)ABC. Also find the length of AD.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Area of triangle = \(\frac{1}{2} \) × base ×height

\(\therefore \) \(\frac{1}{2} \) ×AB×AC = \(\frac{1}{2} \)×BC×AD

Or, \(\frac{1}{2} \)× 5 ×12 = \(\frac{1}{2} \)×13×AD

Or, AD = \(\frac{60}{13} \) = 4.62 cm

Q.8 \(\triangle \)ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC, is 6 cm. Find the area of ?ABC. What will be the height from C to AB i.e., CE?

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Area of \(\triangle \)ABC = \(\frac{1}{2} \) × base × height

\(\therefore \) \(\frac{1}{2} \)×AB×CE= \(\frac{1}{2} \)×BC×AD

Or, \(\frac{1}{2} \)× 7.5× CE = \(\frac{1}{2} \)× 9×6

Or, CE= \(\frac{54}{7.5} \)= 7.2 cm

Q.1 Find the circumference of the circles with the following radius. (Take \(\pi =\frac{22}{7} \))

(a) 14 cm

(b) 28 mm

(c) 21 cm

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

(a) Given: Radius (r) = 14 cm

Circumference =\( 2\pi r = 2 × \frac{22}{7} × 14
= 88 cm \)

(b) Given: Radius (r) = 28 mm

Circumference =\( 2\pi r = 2 × \frac{22}{7} × 28
= 176 mm \)

(c) Given: Radius (r) = 21 cm

Circumference = \( 2\pi r = 2 × \frac{22}{7} × 21
= 132 cm \)

Q.2 Find the area of the following circles, given that (Take \(\pi =\frac{22}{7} \))

(a) radius = 14 mm

(b) diameter = 49 m

(c) radius = 5 cm

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

(a) Given, r = 14 mm
\(\therefore \) Area of the circle =\( \pi r^2 \)

= \(\pi × 14 × 14 = \frac{22}{7} × 14 × 14 = 616mm^2\)

(b) Given, r = 49 m
\(\therefore \)Area of the circle =\(\pi r^2 \)

= \(\pi × 49 × 49 = \frac{22}{7} × 49 × 49= 1886.5 m^2 \)

(c) Given, r = 5 cm
\(\therefore \) Area of the circle =\( \pi r^2 \)

= \(\pi × 5 × 5 = \frac{22}{7} × 5 × 5= 78.57 cm^2 \)

Q.3 If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take \(\pi =\frac{22}{7} \))

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Circumference = 154 m

\(\therefore 2 \pi r = 154 \)

Or, \( 2 × \frac{22}{7} × r = 154 \)

Or, r = \(\frac{154×7}{2×22} = \frac{49}{2} m \)

\(\therefore \) area of circle =\( \pi r^2 = \frac{22}{7} × \frac{49}{2}×\frac{49}{2} \)

= \(\frac{3773}{2} m^2 = 1886.5 m^2 \)

Q.4 A gardener wants to fence a circular garden of diameter 21m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs Rs. 4 per meter. (Take \(\pi = \frac{22}{7} \))

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Diameter of the circular garden = 21 m

\(\therefore Radius = \frac{21}{2} \) m

\(\therefore \)Circumference =\( 2\pi r = 2×\frac{22}{7}×\frac{21}{2}
= 66 m \)

Length of rope needed for 2 rounds
= 2 × 66 m = 132 m

Cost of the rope = Rs. 4 × 132 = Rs. 528

Q.5 From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take \(\pi \)= 3.14)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Radius of the circular sheet = 4 cm

Radius of the circle to be removed = 3 cm

Area of the remaining sheet = area of ring = \( \pi (R^2-r^2)\)

\( = 3.14 (4^2-3^2) = 3.14 × (16-9) = 3.14× 7 = 21.98 cm^2 \)

Hence, the required area = 21.98 \(cm^2.\)

Q.6 Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one metre of the lace costs Rs.15. (Take \(\pi \)= 3.14)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Diameter of the table cover = 1.5 m

\(\therefore \)Radius\( =\frac{1.5}{2}= 0.75 m \)

\(\therefore \)Length of the lace \(= 2\pi r = 2 × 3.14 × 0.75 = 4.71 m \)

Cost of the lace = Rs. 15 × 4.71 = Rs. 70.65

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Diameter = 10 cm

Then r = 5 cm

Perimeter of the adjoining figure = \( \frac{2 \pi r}{2} + 2r = \pi r + 2r \)

\(= \frac{22}{7} × 5 + 2×5 = \frac{110}{7} + 10 = \frac{180}{7} cm \) = 25.71 cm

Q.8 Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs.15\( m^2. (Take \pi = 3.14) \)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Diameter = 1.6 m

\(\therefore Radius = \frac{1.6}{2} = 0.8 m \)

Area of the table-top =\( \pi r^2\)

= 3.14 × 0.8 × 0.8 \(m^2\)

= 2.0096 \(m^2\)

\(\therefore \) Cost of polishing = Rs. 15 × 2.0096

= Rs. 30.144 (approx.)

Q.9 Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take \(\pi =\frac{22}{7} \))

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Length of the wire to be bent into a circle = 44 cm

2\(\pi \)r = 44 cm

Or, 2 ×\(\frac{22}{7} \) × r = 44 cm

Or, r = \(\frac{44×7}{22×2} \)

Area of circle \(\pi r^2 = \frac{22}{7} × 7×7 = 154 cm^2 \)

Now, the length of the wire is bent into a square.

Here perimeter of square= 44cm

Length of each side of the square

= Perimeter/ 4=44/4=11cm

Area of the square = \((Side)^2 = (11)^2 = 121 cm^2 \)

Since, \( 154 cm^2 >121 cm^2 \)

Thus, the circle encloses more area.

Q.10 From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed, (as shown in the given figure below). Find the area of the remaining sheet. (Take \(\pi = \frac{22}{7} \) )

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Radius of the circular sheet = 14 cm

\(\therefore Area = \pi r^2 =\frac{22}{7} × 14 × 14 cm^2
= 616 cm^2 \)

Area of 2 small circles \( = 2 × \pi × r^2 \)

\( = 2 × \frac{22}{7} × 3.5 × 3.5 cm^2 \)
= 77.0 \( cm^2 \)

Area of the rectangle = l × b

=\( 3 × 1 cm^2 = 3 cm^2 \)

Area of the remaining sheet after removing the 2 circles and 1 rectangle

= \( 616 cm^2 – (77 + 3) cm^2 \)

= \( 616 cm^2 – 80 cm^2 = 536 cm^2 \)

Q.11 A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take \(\pi = 3.14)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Side of the square sheet = 6 m

\(\therefore Area of the sheet = (Side)^2 = (6)^2 = 36 cm^2 \)

Radius of the circle = 2 cm

\(\therefore area of the circle to be cut out = ?r^2 \)

=\( \frac{22}{7}×2×2=\frac{88}{7}cm^2 \)

Area of the left over sheet = \( 36cm^2 - \frac{88}{7} cm^2 \)

\(\frac{252-88}{7} cm^2 = \frac{164}{7} cm^2 = 23.44 cm^2

Q.12 The circumference of a circle is 31.4 cm. Find the radius and the area of the circle. (Take \(\pi \) = 3.14)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Circumference of the circle = 31.4 cm

2\(\pi\)r = 31.4

\(\therefore r= \frac{31.4}{2×3.14} = 5cm \)

Area of the circle =\( \pi r^2 = 3.14 × 5 × 5 = 78.5 cm^2 \)
Hence, the required radius = 5 cm and area =\( 78.5 cm^2.\)

Q.13 A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (Take \(\pi \) = 3.14)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Diameter of the flower bed = 66 m .

\(\therefore Radius (r) = 66/2 = 33 m \)

Width of the path = 4 m

Radius of the flower bed included path

(R )= 33 m + 4 m = 37m

Area of the circular path = \(\pi(R^2?r^2) \)

\( = 3.14 (37^2– 33^2) = 3.14 × (37 + 33) (37 – 33) \)

\( = 3.14 × 70 × 4 = 879.20 m^2 \)

\( Hence, the required area = 879.20 m^2 \)

Q.14 A circular flower garden has an area of\( 314 m^2. \) A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler can water the entire garden? [Take\(\pi \) = 3.14]

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Area of the flower garden =\( 314 m^2 \)
Radius of the circular portion covered by the sprinkler = 12 m

\(\therefore area = \pi r^2 = 3.14 × 12 × 12 = 3.14 × 144 m^2 = 452.16 m^2 \)

Since\( 452.16 m^2 > 314 m^2 \)

Yes, the sprinkler will water the entire garden.

Q.15 Find the circumference of the inner and the outer circles, shown in the given figure. (Take \(\pi \)= 3.14)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Radius of the outer circle = 19 m

\(\therefore Circumference of the outer circle = 2\pi r \)

= 2 × 3.14 × 19 = 3.14 × 38 m = 119.32 m

Radius of the inner circle = 19m – 10m = 9m

\(\therefore Circumference = 2 \pi r = 2 × 3.14 × 9
= 56.52 m \)

Here the required circumferences are 56.52 m and 119.32 m.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Radius of the wheel = 28 cm

\(\therefore Circumference = 2\pi r = 2 × \frac{22}{7} × 28 = 176 cm \)

Number of rotations made by the wheel in going 352 m or 35200 cm

\( =\frac{35200}{176} \)=200

Hence, the required number of rotation = 200.

Q.17 The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour? (Take \(\pi \) = 3.14)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Length of minute hand = 15 cm

\(\therefore \)Radius = 15 cm

Circumference = 2\(\pi \) r = 2 × 3.14 × 15 cm = 94.2 cm

Since the minute hand covers the distance in 1 hour equal to the circumference of the circle. Here the required distance covered by the minute hand = 94.2 cm.

Q.1 A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Given: Length = 90 m

Breadth = 75 m

Area of the garden = l × b

= 90 m × 75 m = 6750\( m^2 \)

Length of the garden including path

= 90m + 5m + 5m = 100 m

Breadth of the garden including path

= 75m + 5m + 5m = 85m

Area of the garden including path
= l × b

= 100 m × 85 m = 8500 \( m^2 \)

Area of the path = 8500 \( m^2 – 6750 m^2 = 1750 m^2 \)

Hence, required area of path = \(1750 m^2\) and area of the garden =\( 6750 m^2 = 0.675 hactare \)

Q.2 . A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Length of the park = 125 m

Breadth of the park = 65 m

Area of the park = l × b

= 125 m × 65 m = \( 8125 m^2 \)

Length of the park including path
= 125 m + 3m + 3m = 131 m

Breadth of the park including path
= 65m + 3m + 3m = 71m

Area of the park including path
= 131 m × 71 m = \( 9301 m^2 \)

\(\therefore \)Area of the path\(= 9301 m^2 – 8125 m^2 = 1176 m^2 \)

Hence, the required area =\( 1176 m^2. \)

Q.3 A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1. 5 cm along each of its sides. Find the total area of the margin.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Length = 8 cm, breadth = 5 cm

Area of the cardboard = l × b
\( = 8 cm × 5 cm = 40 cm^2\)

Width of the margin = 1.5 cm

Length of the inner cardboard= 8 cm – 1.5 × 2 cm

= 8 cm – 3 cm = 5 cm

Breadth of the inner cardboard= 5 cm – 1.5 × 2 cm

= 5 cm – 3 cm = 2 cm

Area of the inner rectangle = l × b

= 5 cm × 2 cm = 10 \(cm^2 \)

Area of the margin\(= 40 cm^2 – 10 cm^2 = 30 cm^2 \)
Hence, the required area = 30\( cm^2\)

Q.4 A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find:

(i) the area of the verandah.

(ii) the cost of cementing the floor of the verandah at the rate of Rs. 200 per \( m^2. \)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Length of the room = 5.5 m

Breadth of the room = 4 m

\(\therefore \) Area of the room = l × b = 5.5 m × 4 m = 22 \( m^2 \)

Width of the verandah = 2.25 m

Length of the room including verandah

= 5.5 m + 2 × 2.25 m = 10 m

Breadth of the room including verandah

= 4 m + 2 × 2.25 m = 8.50 m

Area of the room including verandah = l × b

= 10 m × 8.50 m =\( 85 m^2 \)

Q.5 A path 1 m wide is built along the border and inside a square garden of side 30 m. Find:

(i) the area of the path

(ii) the cost of planting grass in the remaining portion of the garden at the rate of Rs. 40 per \( m^2.\)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Area of the square garden =\( (Side)^2 \)

= 30 m × 30 m =\( 900 m^2 \)

Length of the garden excluding the path = 30 m – 2 × 1 m = 28 m

\(\therefore \)Area of the garden excluding the path = 28 m × 28 m = 784\( m^2 \)

(i) Area of the path =\( 900 m^2 – 784 m^2
= 116 m^2 \)

(ii) Cost of the planting the remaining portion

at the rate of Rs. 40 per\( m^2 \)
= Rs. 40 × 784 = Rs. 31,360

Q.6 Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Length of the road parallel to the length of the park = 700 m

Width of the road = 10 m

\(\therefore \) Area of the road = l × b = 700 m × 10 m = 7000\( m^2 \)

Length of the road parallel to the breadth of the park = 300 m

Width of the road = 10 m Area of this road = l × b = 300 m × 10 =\( 3000 m^2 \)

Area of the both roads
= \( 7000 m^2 + 3000 m^2 \)– Area of the common portion

=\( 10,000 m^2 – 10 m × 10 m = 10,000 m^2 – 100 m^2 \)

\(= 9900 m^2 = 0.99 hactare \)

Area of the park = l × b = 700 m × 300 m = \(210000 m^2 \)

Area of the park without the roads

=\( 210000 m^2 – 9900 m^2 \) =\( 200100 m^2 = 20.01 hactare \)

Q.7 Through a rectangular field of length 90 m and breadth 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3 m, find

(i) the area covered by the roads.

(ii) the cost of constructing the roads at of the rate of Rs. 110 per\( m^2. \)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Length of the road along the length of the field = 90 m
Breadth = 3 m

\(\therefore Area of this road = l × b

= 90 m × 3 m =\( 270 m^2 \)

Similarly, the area of the road parallel to the breadth of the field = l × b

= 60 m × 3 m =\( 180 m^2\)

Area of the common portion
=\( 3m × 3m = 9m^2\)

(i) Area of the two roads
= \(270 m^2 + 180 m^2 – 9 m^2 \) =\( 450 m^2 – 9 m^2 = 441 m^2 \)

(ii) Cost of constructing the roads

= Rs. 110 × 441 = Rs. 48,510

Q.8 Pragya wrapped a card around a circular pipe of radius 4 cm and cut off the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any cord left? (\(\pi \)= 3.14)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Length of the cord = Circumference of the circular pipe

= 2\(\pi \)r = 2 × 3.14 × 4 = 25.12 cm

Perimeter of the square box

= 4 × side = 4 × 4 cm = 16 cm

Length of the cord left

= 25.12 cm – 16 cm = 9.12 cm

Yes, 9.12 cm cord is left.

Q.9 The given figure represents a rectangular lawn with a circular flower bed in the middle. Find:

(i) the area of the whole land.

(ii) the area of the flower bed.

(iii) the area of the lawn excluding the area of the flower bed.

(iv) the circumference of the flower bed.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

(i) Length of the lawn = 10 m

Breadth of the lawn = 5 m

Area of the lawn = l × b

=\( 10 m × 5 m = 50 m^2\)

(ii) Area of the circular flower bed = \(\pi r^2 \)

=\(\frac{22}{7} ×2×2=\frac{88}{7}m^2=12.57m^2 \)

(iii) Area of the lawn excluding the area of the flower bed

= \( 50m^2 - \frac{88}{7} m^2 = \frac{350-88}{7} m^2 = \frac{262}{7} \)
= \( 37. 43m^2 \)

(iv) circumference of the flower bed = 2\(\pi r \)

= \( 2 \frac{22}{7} ×2 m^2 = \frac{88}{7} m^2 = 12.57 m^2 \)

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

(i) Area of the rectangle = l × b

= 18 cm × (6 cm + 4 cm) = 18 cm × 10 cm =\( 180 cm^2\)
Area of right triangle \(\triangle \)AEF

=\(\frac{1}{2} ×b×h= \frac{1}{2} ×6×10=30 cm^2 \)

Area of right \(\triangle BCE = \frac{1}{2} × b × h
= \frac{1}{2} × 8 × 10 =40 cm^2 \)

Area of the two right triangles
=\( 30 cm^2 + 40 cm^2 = 70 cm^2 \)

Area of the shaded portion

= \( 180 cm^2 – 70 cm^2 = 110 cm^2 \)

(ii) Area of the square PQRS =\( (Side)^2
= (20)^2 = 400 cm^2 \)

Area of right triangle \(\triangle \)TSU

=\(\frac{1}{2} ×b×h= \frac{1}{2} ×10×10=50 cm^2 \)

Area of right triangle \(\triangle \)QRU

=\(\frac{1}{2} ×b×h= \frac{1}{2} ×20×10=100 cm^2 \)

Area of right triangle \(\triangle \)PQT

=\(\frac{1}{2} ×b×h= \frac{1}{2} ×20×10=100 cm^2 \)

Area of the three triangles

\( = 50 cm^2 + 100 cm^2 + 100 cm^2 = 250 cm^2 \)

Area of the shaded portion

=\( 400 cm^2 – 250 cm^2 = 150 cm^2 \)

Q.11 Find the area of the quadrilateral ABCD. Here, AC = 22 cm, BM = 3 cm, DN = 3 cm, and BM \(\perp \)AC, DN \(\perp \)AC.

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter And Area

Answer :

Area of \(\triangle ABC = \frac{1}{2} × b×h = \frac{1}{2}×22×3 = 33^2 \)

Area of \(\triangle ADC = \frac{1}{2} × b×h = \frac{1}{2}×22×3 = 33^2 \)

Area of the quadrilateral ABCD

= Area of \(\triangle \)ABC + Area of \(\triangle \)ADC
\( = 33 cm^2 + 33 cm^2 = 66 cm^2 \)

Hence, the required area = \(66 cm^2. \)

There are total 44 questions present in ncert solutions for class 7 maths chapter 11 perimeter and area

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