Haryana State Board HBSE 7th Class Maths Solutions Chapter 11 Perimeter and Area Ex 11.4 Textbook Exercise Questions and Answers.

## Haryana Board 7th Class Maths Solutions Chapter 11 Perimeter and Area Exercise 11.4

Question 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.

Solution:

Area of the garden = l x b

= 90 x 75 m^{2} = 6750 m^{2}

= \(\frac{6750}{10000}\)hectare = 0.675 hectare.

Area of the rect angle PQRS = l x b

= (90 + 5 + 5) x (75 + 5 + 5)

= 100 m x 85 m = 8500 m^{2}

= \(\frac{8500}{10000}\) hectare = 0.850 hectare

∴ Area of the path = Area of the recangle PQRS – Area of the rectangle ΔBCD

= 0.850 hect – 0.675 hect.

∴ 8500-6750 = 1750 m^{2}

= 0.175 hectare.

Question 2.

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

Solution:

For outside rectangle

Length = 125 + 3 + 3 = 131 m

Breadth = 65+ 3 + 3 = 71 m

Area of external rectangle = 131 x 71 = 9301 m^{2}.

For internal rectangle

Length = 125 m

Breadth = 65 m

Area of inner rectangle

= 125 x 65 = 8125 m^{2}

Area of path = 9301 – 8125 = 1176 m^{2}.

Question 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.

Solution:

Let us represent the card board of length 8 cm and width 5 cm by the rectangle ABCD, and the painting by the rectangle EFGH as shown in Fig.

∵ AB = 8 cm, BC = 5 cm

∴ EF = (8-2 x 1.5) cm

= (8 – 3) cm = 5 cm

and FG = (5 — 2 x 1.5) cm

= (5 – 3) cm = 2 cm

∴ area of margin

= Area of rectangle ABCD – Area of rectangle EFGH.

= 8 cm x 5 cm – 5 cm x 2 cm

= 40 cm^{2} – 10 cm^{2} = 30 cm^{2}.

Question 4.

A verandah of width 2.25 m is constructed all along outside room which 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 ofRs. 200 per m^{2}.

Solution:

Let us represent the room 5.5 m long and 4 m wide by the rectangle ABCD and the verandah 1.25 m wide all along the outside of the room by the rectangle EFGH as shown in Fig. 11.44.

Now, EF = 2.25 m + 5.5 m + 2.25 m = 10 m

and FG = 2.25 + 4 m + 2.25 m = S.5 m

Therefore the area of the verandah,

= Area of rectangle EFGH – Area of rectangle ABCD

= 10 m x 8.5 m – 5.5 m x 4 m

= 85.0 m^{2} – 22.0 m^{2} = 63 m^{2}.

Rate of cementing of the floor = Rs. 200 per sq. m.

∴ total cost of cementing = Rs. 200 x 63

= Rs. 6000. =Rs. 12,600.

Question 5.

A path 1 m wide is built along the border 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^{3}.

Solution:

Let us represent the square garden of side 30 m by the square ABCD and the path along the border by shaded region as shown as Fig. 11.48.

Area of the remaining portion of the garden = Area of square EFGH

Now, side of square EFGH

= (30 – 2 x 1) m = 28 m

So, the area of the remaining portion of garden = 28 m. x 28 m = 784 m^{2}.

Because, rate of covering the remaining

portion of the garden by grass

= Rs, 40.00 per m^{2}.

∴ Cost of covering it by grass = Rs. 40.00 x 784 = Rs. 31360.00.

Question 6.

Two cross

roads, each of width 10 m, cut at right angles through the centre of a rectangular park of ?

the length 700 m and the breadth 300 m and parallel to its sides. Find the area of the roads. Also find the area of park excluding cross roads. Give the answer in hectares.

Solution:

Length = 700 m

Breadth = 300 m

Area of road parallel to length

= 700 x 10 = 7000 m^{2}

Area of road parallel to breadth

= 300 x 10 = 3000 m^{2}

Area-of common square = 10 x 10 = 100 m^{2}

∴ Area of roads = 7000 + 3000-100 = 9900 m^{2}.

Now, the area of park excluding the cross

road

= (Area of rectangular park – Area of roads)

= [(700 x 300) m^{2}-9900 m^{2}]

= (210000 m^{2}-9900 m^{2})

= 200,100 m^{2}.

∵ 10000 m^{2} = 1 hectare

∴ 1m^{2} = \(\frac{1}{10000}\) hectare

∴ 200100 m^{2} = \(\frac{1}{10000}\) x 200100

= \(\frac{2001}{100}\) = 20.01 hec

= 20.01 hectare.

Question 7.

Through „ a rectangular Held of the length 90 m and the 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 the rate ofRs. 110 per cm^{2}.

Solution:

For field Length = 90 m

Breadth = 60 m

width of road = 3m

Area of road parallel to length

= 90 x 3 = 270 m^{2}

Area of road parallel to breadth

= 60 x 3 = 180 m^{2}

Area of common square = 3 x 3 = 9 m^{2}

(i) Area of roads = 270 + 180 – 9 = 441 m^{2}

(ii) Rate of construction = Rs. 110 per m^{2}

Cost of constructing roads = 110 x 441 = Rs. 48510.

Question 8.

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

Solution:

Circumference of circulare pipe

= 2πr

= 2 x 3.14 x 4 [∵ r = 4]

= 25.12 cm

Perimeter of circular pipe

= 4 x side

= 4 x 4 cm = 16 cm

Cordleft = 25.12 — 16 = 9.12cm

Question 9.

The Fig.

11.49, 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.

Solution:

(i) The area of whole rectangular lawn = l x b

length = 5m

breadth = 10 m

∴ area of the whole rectangular lawn

= l x b = 5 x 10 = 50 m^{2}.

(ii) Area of circular flower bed = πr^{2}

= 22 x (1)^{2}

[r = \(\frac{\mathrm{d}}{2}=\frac{2}{2}\) = 1m]

= 22 m^{2}.

(iii) Area of lawn excluding area of flower bed

= [(Area of rectangular whole land) – (Area of circular flower bed)]

= (50 – 20) m^{2} = 30 m^{2}.

(iv) Circumference of flower-bed = 2πr

= 2 x \(\frac{22}{7}\) x 1 = \(\frac{44}{7}\) = 6.28 m (approx.)

Question 10.

Find the area of shaded portion.

Solution:

(i) Area of rectangle ABCD = l x b

length = 10 cm

breadth = 18 cm

∴ area of rectangle = 10 x 18 = 180 cm^{2}.

Now,area of ΔEAF

= \(\frac{1}{2}\) b x h = \(\frac{1}{2}\) x 6 x 10

= \(\frac{60}{2}\) = 30 cm^{2},

and area of of ΔEBC

= \(\frac{1}{2}\) b x h = \(\frac{1}{2}\) x 8 x 10

= \(\frac{80}{2}\) = 40 cm^{2},

Area of shaded portion

= [(Area of rectangle ΔBCD) – (Area of ΔEAF + area of ΔEBC)]

= [(180)-(40 + 30)3 = [180 — 70] = 110 cm^{2},

(ii) Area of squares PQRS = Side x side side = 20 cm

∴ area of square = 20 x 20 = 400 cm^{2}.

Now,area of ΔTSU

= \(\frac{1}{2}\) b x h = \(\frac{1}{2}\) x 10 x 10

= \(\frac{100}{2}\) = 50cm^{2}

Now,area of ΔQPT

= \(\frac{1}{2}\) b x h = \(\frac{1}{2}\) x 10 x 20

= \(\frac{200}{2}\) = 100cm^{2}

andarea of ΔQRU

= \(\frac{1}{2}\) b x h = \(\frac{1}{2}\) x 10 x 20

= \(\frac{200}{2}\) = 100cm^{2}

Area of shaded portion = [(Area of square PQRS) – (Area of ΔTSU) + (Area of ΔQPT) + (Area of ΔQRU)]

= [(400) – (50 + 100 + 100)] cm^{2}

= (400 – 250) cm^{2} = 150 cm^{2}.

Question 11.

Find the area of the quadrilateral ABCD. Here, AC = 22 cm, BM = 3 cm, DN = 3 cm, and BM ⊥ AC, DN ⊥ AC.

Solution:

In AABC, height = 3 cm base = 22 cm

∴ area of ΔABC = \(\frac{1}{2}\) x b x h

= \(\frac{1}{2}\) x 22 x 3

= \(\frac{66}{2}\) = 33 m^{2}

And area ΔADC,

height = 3 cm

base = 22 cm

∴ area of ΔADC = \(\frac{1}{2}\) x b x h

\(\frac{1}{2}\) x 22 x 3 = \(\frac{66}{2}\) = 33 m^{2}

∴ Area of quadrilaterial ABCD = Area of ΔABC + Area ΔADC

= (33 + 33) cm^{2} = 66 cm^{2}.