MENSURATION PART 1 (2D) EXAMPLE QUESTIONS

MENSURATION PART 1(2D) EXAMPLE QUESTIONS:

 

1. What is the are of an equilateral triangle of side 16 cm?

A. 48√3 cm2

B. 128√3 cm2

C. 9.6√3 cm2

D. 64√3 cm2

E. None of these

 

Answer & Explanation

Answer: Option D

Explanation:

Area of an equilateral triangle = √3/4 S^2

If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm^2;

 

2. If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?

A. 120 cm2

B. 130 cm2

C. 312 cm2

D. 315 cm2

E. None of thesae

 

Answer & Explanation

Answer: Option A

Explanation:

The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.

Area of the triangle = 1/2 * 24 * 10 = 120 cm2

 

3. The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?

A. 25 cm2

B. 42 cm2

C. 49 cm2

D. 70 cm2

E. None of these

 

Answer & Explanation

Answer: Option E

Explanation:

Area of a triangle = r * s

Where r is the inradius and s is the semi perimeter of the triangle.

Area of triangle = 2.5 * 28/2 = 35 cm2

 

 

4. Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.

A. 225 cm2

B. 275 cm2

C. 285 cm2

D. 315 cm2

E. None of these

Answer & Explanation

Answer: Option C

Explanation:

Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)

= 1/2 (20 + 18) * (15) = 285 cm2

 

 

5. Find the area of a parallelogram with base 24 cm and height 16 cm.

A. 262 cm2

B. 384 cm2

C. 192 cm2

D. 131 cm2

E. None of these

 

Answer & Explanation

Answer: Option B

Explanation:

Area of a parallelogram = base * height = 24 * 16 = 384 cm2

 

6. The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?

A. 1 : 96

B. 1 : 48

C. 1 : 84

D. 1 : 68

E. None of these

 

 

Answer & Explanation

Answer: Option A

Explanation:

 

Let the length and the breadth of the rectangle be 4x cm and 3x respectively.

 

(4x)(3x) = 6912

12x^2 = 6912

x^2 = 576 = 4 * 144 = 2^2 * 12^2 (x > 0)

=> x = 2 * 12 = 24

Ratio of the breadth and the areas = 3x : 12x^2 = 1 : 4x = 1: 96.

 

 

7. The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?

A. 8

B. 12

C. 6

D. 2

E. None of these

 

Answer & Explanation

Answer: Option D

Explanation:

 

Let the sides of the rectangle be l and b respectively.

 

From the given data,

(√l^2 + b^2) = (1 + 108 1/3 %)lb

=> l^2 + b^2 = (1 + 325/3 * 1/100)lb

= (1 + 13/12)lb

= 25/12 lb

=> (l^2 + b^2)/lb = 25/12

12(l^2 + b^2) = 25lb

Adding 24lb on both sides

12l^2 + 12b^2 + 24lb = 49lb

12(l^2 + b^2 + 2lb) = 49lb

but 2(l + b) = 28 => l + b = 14

12(l + b)^2 = 49lb

=> 12(14)^2 = 49lb

=> lb = 48

Since l + b = 14, l = 8 and b = 6

l - b = 8 - 6 = 2m.

 

 

8. The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?

A. 8.5 m

B. 17 m

C. 34 m

D. 51 m

E. None of these

 

 

Answer & Explanation

Answer: Option B

Explanation:

 

Let the breadth of the plot be b m.

Length of the plot = 3 b m

(3b)(b) = 867

3b^2 = 867

b^2 = 289 = 17^2 (b > 0)

b = 17 m.

 

9. The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?

A. 27 m

B. 24 m

C. 18 m

D. 21 m

E. None of these

 

Answer & Explanation

Answer: Option C

Explanation:

 

Let the length and the breadth of the floor be l m and b m respectively.

l = b + 200% of b = l + 2b = 3b

Area of the floor = 324/3 = 108 sq m

l b = 108 i.e., l * l/3 = 108

l^2 = 324 => l = 18.

 

 

10. An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?

A. Rs. 3642.40

B. Rs. 3868.80

C. Rs. 4216.20

D. Rs. 4082.40

E. None of these

 

Answer & Explanation

Answer: Option D

Explanation:

 

Length of the first carpet = (1.44)(6) = 8.64 cm

Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)

= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m

Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40

 

11. What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?

A. Rs. 3944

B. Rs. 3828

C. Rs. 4176

D. Cannot be determined

E. None of these

 

Answer & Explanation

Answer: Option A

Explanation:

 

Let the side of the square plot be a ft.

 

a^2 = 289 => a = 17

Length of the fence = Perimeter of the plot = 4a = 68 ft.

Cost of building the fence = 68 * 58 = Rs. 3944.

 

12. The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?

A. 600 cm

B. 800 cm

C. 400 cm

D. 1000 cm

E. None of these

 

Answer & Explanation

Answer: Option B

Explanation:

 

Area of the square = s * s = 5(125 * 64)

=> s = 25 * 8 = 200 cm

Perimeter of the square = 4 * 200 = 800 cm.

 

13. A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?

A. 60 cm2

B. 30 cm2

C. 45 cm2

D. 15 cm2

E. None of these.

 

Answer & Explanation

Answer: Option B

Explanation:

 

The circumference of the circle is equal to the permeter of the rectangle.

Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5

 =>  x = 1

Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2

 

14. The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.

A. 18 : 5

B. 7 : 16

C. 5 : 14

D. 5 : 32

E. None of these.

 

Answer & Explanation

Answer: Option E

Explanation:

 

Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.

 

a2 = 4096 = 2612

a = (2^12)1/2 = 2^6 = 64

L = 2a and b = a - 24

b : l = a - 24 : 2a = 40 : 128 = 5 : 16

 

15. The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.

A. 200 sq cm

B. 72 sq cm

C. 162 sq cm

D. Cannot be determined

E. None of these

 

Answer & Explanation

Answer: Option D

Explanation:

 

Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.

 

4a = 2(l + b)

2a = l + b

l . b = 480

We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .

Area of the square cannot be found.

 

 

16. The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.

A. 4192 sq m

B. 4304 sq m

C. 4312 sq m

D. 4360 sq m

E. None of these

 

Answer & Explanation

Answer: Option C

Explanation:

 

Let the radii of the smaller and the larger circles be s m and l m respectively.

 

2∏s = 264 and 2∏l = 352

s = 264/2∏ and l = 352/2∏

Difference between the areas = ∏l^2 - ∏s^2

= ∏{176^2/∏^2 - 132^2/∏^2}

= 176^2/∏ - 132^2/∏

= (176 - 132)(176 + 132)/∏

= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m

 

17. A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is

A. 3.34

B. 2

C. 4.5

D. 5.5

E. 5

 

Answer & Explanation

Answer: Option A

Explanation:

 

Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]^2

= ∏[2.25^2 - 2^2] = ∏(0.25)(4.25)  { (a^2 - b^2 = (a - b)(a + b) }

= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m

 

 

18. The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)

A. 77.14 cm

B. 47.14 cm

C. 84.92 cm

D. 94.94 cm

E. 23.57 cm

 

Answer & Explanation

Answer: Option E

Explanation:

 

Let the side of the square be a cm.

 

Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm

 i.e. 4a = 60

A = 15

Diameter of the semicircle = 15 cm

Circimference of the semicircle

= 1/2(∏)(15)

= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places

 

19. There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.

A. 6∏ cm

B. 8∏ cm

C. 12∏ cm

D. 16∏ cm

E. None of these.

 

Answer & Explanation

Answer: Option C

Explanation:

 

Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.

 

a^2 = 784 = (4)(196) = (2^2).(14^2)

a = (2)(14) = 28

a = 2l, l = a/2 = 14

l = (7/3)s

Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.

 

 

20. A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?

A. 10

B. 100

C. 1000

D. 10000

E. None of these

 

Answer & Explanation

Answer: Option C

Explanation:

 

Along one edge, the number of small cubes that can be cut

= 100/10 = 10

Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000

 

 

21. The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?

A. Rs. 4800

B. Rs. 3600

C. Rs. 3560

D. Rs. 4530

E. None of these

 

Answer & Explanation

Answer: Option D

Explanation:

 

Area of the four walls = 2h(l + b)

Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.

Total cost = 906 * 5 = Rs. 4530

 

 

22. The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.

A. 252 m

B. 704 m

C. 352 m

D. 808 m

E. None of these

 

Answer & Explanation

Answer: Option B

Explanation:

In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.

= 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m

 

23. The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?

A. 2 : 5

B. 1 : 5

C. 3 : 5

D. 4 : 5

 

Answer & Explanation

Answer: Option A

Explanation:

 

The volume of the cone = (1/3)πr2h

Only radius (r) and height (h) are varying.

Hence, (1/3)π may be ignored.

V1/V2 = r12h1/r22h2  => 1/10  =  (1)^2h1/(2)^2h2

=> h1/h2 = 2/5 

i.e. h1 : h2 = 2 : 5

 

 

24. A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?

A. 45 cm

B. 18 cm

C. 90 cm

D. 180 cm

E. None of these

 

Answer & Explanation

Answer: Option E

Explanation:

Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.

 

 π(16)^2 * h = (4/3)π (12)^3 => h = 9 cm

 

25. The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?

A. 81 : 121

B. 9 : 11

C. 729 : 1331

D. 27 : 121

E. None of these

 

Answer & Explanation

Answer: Option A

Explanation:

 

Ratio of the sides = ³√729 : ³√1331 = 9 : 11

Ratio of surface areas = 9^2 : 11^2 = 81 : 121

 

 

26. Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?

A. 225 sq.m

B. 360 sq.m

C. 720 sq.m

D. 480 sq.m

E. None of these

 

Answer & Explanation

Answer: Option E

Explanation:

 

Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.

BE^2 + AE^2 = AB^2

25^2 = 15^2 + AE^2 AE = √(625 - 225) = √400 = 20,

AC = 20 + 20 = 40 cm.

Area of a rhombus = 1/2 * d1d2

= 1/2 * 40 * 30 = 600 sq.cm.

 

27. The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?

A. 140

B. 156

C. 175

D. 214

E. None of these

 

Answer & Explanation

Answer: Option A

Explanation:

 

Given that the area of the square = 1225 sq.units

=> Side of square = √1225 = 35 units

The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units

Given that breadth = 10 units

Area of the rectangle = lb = 14 * 10 = 140 sq.units

 

28. The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?

A. 91.5 cm

B. 93.5 cm

C. 94.5 cm

D. 92.5 cm

E. None of these

 

Answer & Explanation

Answer: Option A

Explanation:

 

Perimeter of the sector = length of the arc + 2(radius)

= (135/360 * 2 * 22/7 * 21) + 2(21)

= 49.5 + 42 = 91.5 cm

 

29. An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.

A. 4 : 3

B. 8 : 7

C. 4 : 1

D. 6 : 5

E. None of these

 

Answer & Explanation

Answer: Option B

Explanation:

 

Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.

Let the dimensions of the carpet in the second case be 7y, 3y units respectively.

 From the data,.

2(3x + 2x) = 2(7y + 3y)

 => 5x = 10y

=> x = 2y

Required ratio of the areas of the carpet in both the cases

= 3x * 2x : 7y : 3y

= 6x^2 : 21y^2

= 6 * (2y)^2 : 21y^2

= 6 * 4y^2 : 21y^2 

= 8 : 7

 

 

30.A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per sq.m is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.

 

A) b=6; l=18; H=6            

B) b=5; l=6; H=18

C) l=6; b=18; H=15          

D) l=5; b=18; H=18

 

Answer: A) b=6; l=18; H=6

 

Explanation:

Let breadth = x metres, length = 3x metres, height = H metres.

Area of the floor=(Total cost of carpeting)/(Rate) = (270/5) sq.m = 54 sq.m

x*3x/2=54⇒x^2=54×2⇒x=6 

So, breadth = 6 m and length =3(6)/2 = 9 m.

Now, papered area = (1720/10) =  172 sq.m

Area of 1 door and 2 windows = 8 sq.m

Total area of 4 walls = (172 + 8) sq.m = 180 sq.m

2×(9+6)H=180⇒H=6

 

 

31. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

 

A.15360

B.153600

C.30720

D.307200

Answer: Option B

Explanation:

 

Perimeter = Distance covered in 8 min. =12000/60x 8m = 1600 m.

Let length = 3x metres and breadth = 2x metres.

Then, 2(3x + 2x) = 1600 or x = 160.

Length = 480 m and Breadth = 320 m.

Area = (480 x 320) m^2 = 153600 m^2.

 

 

32. An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

 

A.2%

B.2.02%

C.4%

D.4.04%

Answer: Option D

Explanation:

100 cm is read as 102 cm.

A1 = (100 x 100) cm^2 and A2 (102 x 102) cm^2.

(A2 - A1) = [(102)^2 - (100)^2]

= (102 + 100) x (102 - 100)

= 404 cm2.

Percentage error =(404/100 x 100)x 100 %= 4.04%

 

 

33. A wire is in the form of a circle. The radius of the circle is 28 cm. The wire is then moulded to form a square. Find the side of the square formed?

A.  44 cm

B.  66 cm

C.  22 cm

D.  11 cm

 

 

Answer: (A).

Explanation:

Radius of the circle (r) = 28 cm.

Length of the wire (Circumference) = 2πr=2π28=176 cm

Let side of the square be 'a' cm.

Perimeter of square (4a) = Circumference of the circle = 176 cm

or, 4a = 176 cm

or, a = 44 cm

Thus, side of the square is 44 cm.

 

 

34. The breadth of a rectangular field is 75% of its length. If the perimeter of the field is 1,050 m, then area of the field is:

A.  65,000 m^2

B.  62,000 m^2

C.  67,500 m^2

D.  68,500 m^2

Answer: (C).

Explanation:

 

Let length of the rectangular field be x m.

 

∴ breadth = 75% of x = 3x/4

Perimeter of rectangular field = 1050

or, 2(length + breadth) = 1050

or, 2(x+3x/4)=1050

or, 7x = 1050 * 2

or, x = 300 m

∴ Length = 300 m

Breadth=3x/4=3∗300/4=225m

∴ Area = length * Breadth = 300 * 225 = 67500 m^2

 

 

35. In a square field the diagonal is 30 m. What is the area of the square field?

A.  90 m^2

B.  500 m^2

C.  450 m^2

D.  60 m^2

Answer: (C).

Explanation:

 

When diagonal is given, Area of square = (diagonal)2 divided by 2

 

∴ Area=30∗30/2=450 m^2

 

 

36. The area of the path 1 m wide surrounding a playground 60 m long and 40 m broad is:

A.  200 sq. m.

 

B.  204 sq. m.

 

C.  2604 sq. m.

 

D.  240 sq. m.

 

 

Answer: (B).

Explanation:

Length of the playground (L1) = 60 m

Breadth of the playground (B1) = 40 m

∴ area of the playground = length * breadth = 60 * 40 = 2400 sq. m

Also,

Length of the playground including length of the path (L2) = 60 + 2 = 62 m

Breadth of the playground including length of the path (B2) = 40 + 2 = 42 m

∴ area of the playground including area of the path = 62 * 42 = 2604 sq. m

Thus, area of the path = 2604 - 2400 = 204 sq. m

 

37. A restaurant hall is 20 metre long, 15 metre wide and 5 metre high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square metre?

A.  Rs. 64000

B.  Rs. 57000

C.  Rs. 52000

D.  Rs. 45000

 

Answer: (B).

Explanation:

Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m

Total area of the hall to be covered with mat = 2(lb + bh + hl)

= 2(20 * 15 + 15 * 5 + 5 * 20)

=2(300 + 75 + 100)

= 2 * 475

= 950 sq. m

Total expenditure = 60 * 950= Rs. 57000

38. A circular road runs around a circular ground. If the difference between the circumference of the outer circle and the inner circle is 44 metres, find the width of the road?

A.  8 metres

B.  7 metres

C.  17 metres

D.  9 metres

 

Answer: (B).

Explanation:

 

Let radius of the outer circle be R and radius of the inner circle be r.

Circumference of the outer circle = 2πR

Circumference of the inner circle = 2πr

But, 2πR−2πr=44

or, R - r = 44/2π=44∗74/4=7 m

Thus, width of the road = 7 m.

 

39. The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm * 6 cm * 2 cm is:

A.  2 √ 13

B.  2 √ 14

C.  2 √ 26

D.  10 √ 21

 

Answer: (C).

Explanation:

 

Length of the rectangular box (l) = 8 cm

Breadth of the rectangular box (b) = 6 cm

Height of the rectangualar box (h) = 2 cm

The maximum length of a pencil that can be kept in a rectangular box = √(l2+b2+h2)

= √(8^2+6^2+2^2)=√(64+36+4)=√104=√226

40. What is the cost of levelling the field in the form of parallelogram at the rate of Rs. 50 per 10 sq.metre, whose base and perpendicular distance from the other side being 54 metre and 24 metre respectively?

A.  Rs. 6840

B.  Rs. 6480

C.  Rs. 6450

D.  Rs. 6680

 

Answer: (B).

Explanation:

 

Area of the parallelogram = Length of the base * Perpendicular height

= 54 * 24 = 1296 m.

Total cost of levelling = (Rs.)(1296/10)∗50=Rs. 6480

 

 

41. The perimeter of one square is 24 metres and that of another is 32 metres. Perimeter of a square whose area is equal to the sum of the areas of the two squares will be:

A.  30 m

B.  40 m

C.  50 m

D.  60 m

 

Answer: (B).

Explanation:

 

Perimeter of square = 4 * Side

Perimeter of first square = 24 m.

Side of first square = 24/4=6

∴ Area of first square = (Side)^2=(6)^2=36

Perimeter of second square = 32 m.

Side of second square = 324=8

∴ Area of second square = (Side)^2=(8)^2=64

Sum of the areas of two squares = 36 + 64 = 100 m^2

∴ Side of square = √100−=10 m

∴ Perimeter of square = 4 * 10 = 40 m.

 

42. The three side of a triangle are 3 cm, 4 cm and 5 cm respectively, then its area is:

A.  6 sq.cm

B.  7 sq.cm

C.  8 sq.cm

D.  9 sq.cm

 

Answer: (A).

Explanation:

 

The three sides of the triangle are

a = 3 cm, b = 4 cm and c = 5 cm

∴ S=12(a + b + c)=12(3 + 4 + 5)=6 cm

∴ Area of a triangle =√s(s−a)(s−b)(s−c)

= √(6(6−3)(6−4)(6−5))

= √(6∗3∗2∗1)=6 sq.cm

 

43. One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area of the parallelogram?

 

A.12.56cm^2

B.14.56cm^2

C.16.76cm^2

D.22.56cm^2

 Answer & Explanation

Answer: Option C

 

Explanation:

Area of parallelogram = Base x Height

= 8.06 x 2.08 = 16.76 cm^2

 

44. The length and breadth of a rectangular piece of land are in the ratio of 5 : 3, the owner spent ₹ 3000 for surrounding it from all the sides at ₹ 7.50 per meter. The different between its length and breadth is ?

 

A.50 m

B.100 m

C.150 m

D.200 m

 Answer & Explanation

Answer: Option A

Explanation:

 

Let Length = 5y meters and breadth = 3y meters.

Then, perimeter = 2 x (5y + 3y ) m = 16y meters ...(i)

But perimeter = Total Cost / Rate = 3000 / 7.50 m = 400 m ...(ii)

from eqs. (i) and (ii)

16y = 400

⇒ y = 25

∴ Length - Breadth = (5 x 25 - 3 x 25 ) m

= 2 x 25 m

= 50 m

 

45. The cost of cultivating a square field at the rate of Rs. 160 per hectare is Rs. 1440. the cost of putting a fence around it at 75 paisa per meter is ?

 

A.₹ 900

B.₹ 1800

C.₹ 360

D.₹ 810

 Answer & Explanation

Answer: Option A

Explanation:

Area = 1440 / 160 hectares

= 9 hectares

= 90000 m2

∴ One side = √90000 m

= 300 m

So perimeter = 4 x 300 m

= 1200 m

∴ Cost of fencing = Rs (1200 x 75) / 100

= Rs. 900

 

46. A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?

 

A.100 meters

B.66.66 meters

C.33 meters

D.(100/ √ 3 ) meters

 Answer & Explanation

Answer: Option A

Explanation:

 

Let breadth = b meters.

then, length = 3b/2 meters

∴ b x 3b/2 = 2/3 X 10000

⇒ b^2 = (4 x 10000)/9

⇒ b = ( 2 X 100)/3 m

∴ Length = (3/2) x (2/3) x 100 m

= 100 m

 

47. The length of a plot is four times its breath. A playground measuring 1200 square meters occupies one third of the total area of a plot . what is the length of the plot in meters ?

 

A.20

B.30

C.60

D.None of these

 Answer & Explanation

Answer: Option D

Explanation:

Area of the plot = (3 x 1200) m2

= 3600 m2

Let breadth = y meters

Then Length = 4y meters,

Now area = 4y x y = 3600 m2

⇒ y2 = 900 m2

⇒ y = 30 m

∴ Length of plot = 4y m

= (4 x 30) m

=120 m

 

48. A rectangular piece of paper has an area 840 sq. cm. The length of the side is 48 cm. Therectangle is stretched such that its area becomes 20/7times original rectangle. The only dimension that changes is the breadth of the rectangle. Find the perimeter of the new rectangle.

 

a. 1.69 m

b. 1.85 m

c. 1.96 m

d. 2.25 m

 

Answer: c. 1.96 m

Explanation:

New area =         = 840 x  20           = 2400 sq.cm

Area of Rectangle = length x breadth

New Breadth =  New Area/Length             =2400/48= 50 cm

Perimeter of new margin = 2(length + new breadth) = 2(48 + 50) = 196cm = 1.96m

 

49. The area of a square piece of fabric is same as the area of a circular piece of fabric with diameter 8 cm. Find the perimeter of the square.

 

a. 4π

b. 4π

c. 16π

d. 32

 

Answer: c. 16√π

Explanation:

 

We know,

Area of circle = Area of Square

∴ πr^2 = (side)^2

∴ side = √π x r = √π x       diameter/2          = 4√π

∴ Perimeter of square = 4 x side = 16√π

 

 

50. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

 

A.1520 m2

B.2420 m2

C.2480 m2

D.2520 m2

Answer: Option D

Explanation:

 

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.

Solving the two equations, we get: l = 63 and b = 40.

 Area = (l x b) = (63 x 40) m^2 = 2520 m^2.