23 + Interview Questions in PERIMETER-AND-AREA IN GENERAL AWARENESS Page 1 InterviewSolution

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 m2 of the land costs Rs 10,000.
Answer» Here, length of rectangular piece of land, ` l = 500m` Breadth of rectangular piece of land, `b = 300m` So, Area of rectangular piece of land, `A = 500300 = 150000m^2` Cost of `1m^2` land `=10000` Rs `:.`Cost of `150000m^2` land `= 15000010000 = 15xx10^8` Rs

Discussion

2.	Find the circumference of the circles with the following radius: (Take `22/7`) (a) `14cm` (b) `28mm` (c) `21cm`
Answer» circumference `= 2 pi r` (a) `c= 2 xx 22/7 xx 4` `= 88 cm` (b) c`= 2 xx 22/7 xx 28` `= 176 mm` (c) c `= 2 xx 22/7 xx 21` `= 132 cm` answer

Discussion

3.	The area of a square park is the 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.
Answer» Side of square park , `a = 60m` Length of rectangular park, `l = 90 m` Let breadth of rectangular park is `b` m. As area of both parks are equal, `:. a^2 = lb` `6060 = 90**b=> b = 3600/90 = 40m`

Discussion

4.	The adjoining figure shows two circles with the same centre. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm.
Answer» Here,radius of larger circle, `R = 10` cm Radius of smaller circle, `r = 4` cm (a) `:.` Area of larger circle, `A =piR^2 = 3.141010 = 314 cm^2` (b)Area of smaller circle `a = pir^2 = 3.1444 = 50.24cm^2 ` (c) Area of shaded region ` = A-a = 314-50.24 = 263.76cm^2`

Discussion

5.	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 ? `(pi=3.14)`
Answer» If we create a diagram, we have two circles. One outer circle that is surrounded with `4m` wide path and inner circle that is circular flower bed. Diameter of flower bed ` = 66m` Radius of inner circle(flower bed) ` r = 66/2 = 33m` Radius of outer circle ` R = 33+4 = 37m` So, Area of the path, A = Area of outer circle - Area of inner circle `A = pi(R^2-r^2) = 3.14(37^2 - 33^2) = 280**3.14 = 879.2 m^2`

Discussion

6.	A path 5 m wide runs along inside a square park of side `100 m.` Find the area of the path. Also find the cost of cementing it at the rate of `Rs250` per `10m^2.`
Answer» AB=PQ-5-5=90m BC=90m Area of path=(100100)-(9090) =10000-8100 =1900`m^2` Cementry cost=1900*25=47500Rs.

Discussion

7.	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 m2.
Answer» let PQ is the length of the house `= 5.5 + 2.25 + 2.25 = 10 m` let QR bw the breadth of the house = `4 + 4.5= 8.5 m` area of verandah = area of house `-` area of room area of verandah = `(10 xx 8.5) - (5.5 xx 4)` `= 85 - 22 = 63 m^2` cementing cost of `1m^2` is = `200 rs` cementing cost of `63m^2`= `200 xx 63` `= 12600 rs` answer

Discussion

8.	The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area
Answer» Perimeter of a rectangle, `P = 2(l+b) = 100cm` Here. ` l = ` length` = 35 cm` `b = ` breadth So, `100 = 2(35+b)=> b+35 = 50` `b = 50 -35 = 15cm` So, Area of rectangle, `A = lb = 3515 = 525cm^2`

Discussion

9.	A circular flower garden has an area of `314m^2.` A sprinkler at the centre of the garden can cover an area that has a radius of `12m.` Will the sprinkler water th entire garden ? (Take p`pi=3.14`)
Answer» Area covered by sprinkler, `A = pir^2` `A = 3.141212 = 491m^2` As, `491m^2`(area covered by sprinkler) `gt 314m^2` (area of circular garden), it will water the entire garden.

Discussion

10.	A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path.
Answer» Area of park=`LxxB` where L and B are length and breadth of park. =>`LxxB=45xx30=1350(m)^2` area of bigger rectangle including path=>`L_2xxB_2=(45+2.5)(30+2.5)` =>`47.5xx32.5=1543.75(m)^2` area of path=`1543.75-1350=193.75(m)^2`

Discussion

11.	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.
Answer» Length of garden `= 90 m`Breadth of garden `= 75m`Width of path `= 5m`Outer length `= 100m (90+5+5)`Outer breadth `= 85m (75+5+5)`Area of path = area of outer rectangle - area of inner rectangle`rArr (10085) - (9075)``rArr 8500 - 6750 = 1750 m^2`Hence, area of rectangle 1= 1750 m^21Now, `1 hec = 2592 m^2`Area of path in `hec = 175/2592 = 675`Area of garden in `hec = 6750/2592 = 2.604`

Discussion

12.	`DL and BM` are the height on sides `AB and AD` respectively of parallelogarm `ABCD` (Fing `11.24`). If the area of the parallelogram is `1470cm^2, AB=35cm and AD=49cm` find the `BM and DL.`
Answer» Area = `b xx h` `1470 = 49 xx BM` BM`= 1470/49` `= 30cm` Area = AB `xx` DL `1470 = 35 xx `DL DL`= 1470/35= 210/5` `= 42 cm` Answer

Discussion

13.	One of the sides and the corresponding height of a parallelogram are 4 cm and 3 cm respectively. Find the area of the parallelogram (Fig 11.17).
Answer» Area of a parallelogram, `A = base(b)xxheight(h)` Here, `b = 4cm, h = 3cm` So, Area `A = 4**3 = 12cm^2`

Discussion

14.	The two sides of the parallelogram ABCD are 6 cm and 4 cm. The heightcorresponding to the base CD is 3 cm (Fig 11.19). Find the(i) area of the parallelogram. (ii) the height corresponding to the base AD.
Answer» Area = `b xx h = 6 xx 3 = 18 cm^2` let x be corresponding height from base AD area = `4 xx x = 8 cm^2` `x = 18/4 = 4.5 cm` answer

Discussion

15.	Find the number whose `6.25%` is `20`
Answer» let assume that number be x `x6.25/100=20` `x=(20100*100)/(625)=320`.

Discussion

16.	Anu wants to fence the garden in front of her house (Fig 11.5), on three sides with lengths 20 m, 12 m and 12 m. Find the cost of fencingat the rate of Rs 150 per metre
Answer» total length is `= 20+ 12+ 12` `= 44 m` cost of 1 metre fence `= 150 rs` cost of 44 m fence = `150 xx 44` `= 6600 rs` answer

Discussion

17.	Find the height ‘x’ if the area of the parallelogram is `24 cm^2 `and the base is4 cm.
Answer» As we know, that Area = length `xx` breadth Area `= x xx 4` `24 = x xx 4` `x = 24/4 = 6cm` answer

Discussion

18.	The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is30 cm, find its length. Also find the area of the rectangle.
Answer» Perimeter of rectangle=130cm 2(l+b)=130cm 2(l+30)=130cm 2l=130-60cm 2l=70 l=35cm.

Discussion

19.	Find the perimeter of the given shape (Fig 11.32) (Take `pi/22//7`)
Answer» Perimeter of given shape can be given as circumference of 4 semi circles with diameter `14` cm. `:.` Perimeter, `P = 41/2pid` `P = 41/222/714 = 88cm`

Discussion

20.	A wire is in the shape of a square of side 10 cm. If the wire isrebent into a rectangle of length 12 cm, find its breadth. Which enclosesmore area, the square or the rectangle?
Answer» perimeter of square `= 10 xx 4 = 40cm` perimeter of rectangle = `2(l+b)` `40 = 2(12+b)` `b + 12 = 20` `b = 8cm` area of rectangle = `l xx b` `= 12 xx 8 = 96 cm^2` `area of square = 10^2 = 100 cm^2` `:.`square `>` rectangle answer

Discussion

21.	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? `(Taken pi = (22)/(7))`
Answer» length of wire=44cm. circumference of circle=>`2pir` where r is the radius of circle. =>`2xx22/7xxr=44` =>`r=7cm` =>area of circle=`pir^2`=>`22/7xx7xx7=154(cm)^2` Now the wire is bent into a square...perimeter of square=4s. `4s=44` `s=11cm` Area of square=>`s^2=(11)^2=121(cm)^2` circle has more area than square.

Discussion

22.	A wire bent in the form of a square encloses an area of 121 sq cm. If the same wire is bent in the form of a circle, find the area it enclosed.
Answer» when in square:, area=`a^2 = 121` `a = 11cm` perimeter of square = `11 xx 4 = 44 cm` when in circle, area =`2 pi r = 44` `2 xx 22/7 xx r = 44` `r = 7cm` area = `pi r^2 = 22/7 xx 7 xx 7` `= 154 cm^2` Answer

Discussion

23.	6).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=22/7`)(7).Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find thelength of the lace required and also find its cost if one meter of the lace costs ₹15.(take `pi=22/7`)
Answer» area of 4 cm sheet `= pi(4)^2 ` `= 16 pi` area of 3 cm sheet`= pi(3)^2 = 9 pi` remaining area `= 16 pi - 9 pi` `= 7 pi = 7 xx 3.14` `= 21.98 cm^2` answer

Discussion

Explore topic-wise InterviewSolutions in .

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 m2 of the land costs Rs 10,000.

Find the circumference of the circles with the following radius: (Take `22/7`) (a) `14cm` (b) `28mm` (c) `21cm`

The area of a square park is the 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.

The adjoining figure shows two circles with the same centre. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm.

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 ? `(pi=3.14)`

A path 5 m wide runs along inside a square park of side `100 m.` Find the area of the path. Also find the cost of cementing it at the rate of `Rs250` per `10m^2.`

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 m2.

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

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

A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path.

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.

`DL and BM` are the height on sides `AB and AD` respectively of parallelogarm `ABCD` (Fing `11.24`). If the area of the parallelogram is `1470cm^2, AB=35cm and AD=49cm` find the `BM and DL.`

One of the sides and the corresponding height of a parallelogram are 4 cm and 3 cm respectively. Find the area of the parallelogram (Fig 11.17).

The two sides of the parallelogram ABCD are 6 cm and 4 cm. The heightcorresponding to the base CD is 3 cm (Fig 11.19). Find the(i) area of the parallelogram. (ii) the height corresponding to the base AD.

Find the number whose `6.25%` is `20`

Anu wants to fence the garden in front of her house (Fig 11.5), on three sides with lengths 20 m, 12 m and 12 m. Find the cost of fencingat the rate of Rs 150 per metre

Find the height ‘x’ if the area of the parallelogram is `24 cm^2 `and the base is4 cm.

The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is30 cm, find its length. Also find the area of the rectangle.

Find the perimeter of the given shape (Fig 11.32) (Take `pi/22//7`)

A wire is in the shape of a square of side 10 cm. If the wire isrebent into a rectangle of length 12 cm, find its breadth. Which enclosesmore area, the square or the rectangle?

A wire bent in the form of a square encloses an area of 121 sq cm. If the same wire is bent in the form of a circle, find the area it enclosed.