Q 1-The area of a triangle is with base 4m and height 5m?

A - 20 sq m

B - 10 sq m

C - 5 sq m

D - 3 sq m

Answer - B

Explanation

"Area of a triangle is = 1/2 x Base x Height. 
Given,
Base = 4 m 
and Height = 5 m;
Hence, 
Area of the triangle = 1/2 x 4 x 5 sq.m = 10 sq.m
"

Q 2-The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

A - 9 cm

B - 18 cm

C - 20 cm

D - 41 cm

Answer - B

Explanation

"
√(l2 + b2) = 41.

Also, lb = 20.

(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81

 (l + b) = 9.

 Perimeter = 2(l + b) = 18 cm."

Q 3-What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

A - 814

B - 820

C - 840

D - 844

Answer - A

Explanation

"Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.

Area of each tile = (41 x 41) cm2.

Required number of tiles = 1517×90241×41
1517×90241×41
 = 814
"

Q 4-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 - 2480m2

D - 2520 m2

Answer - 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) m2 = 2520 m2.
"

Q 5-The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

A - 25% increase

B - 50% increase

C - 60% increase

D - 70% increase

Answer - B

Explanation

"Let original length = x and original breadth = y.

Original area = xy.

New length = x/2

New area = x×3y^2= 32
Increase % = ((xy/2) ×[1/ xy]×100)% = 50%
"

Q 6-A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

A - 34

B - 40

C - 68

D - 88

Answer - D

Explanation

"Explanation: 
We have: l = 20 ft and lb = 680 sq. ft.

So, b = 34 ft.

Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.
"

Q 7-A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

A - Rs. 456

B - Rs. 458

C - Rs. 556

D - Rs. 558

Answer - C

Explanation

"Area to be plastered = [2(l + b) x h] + (l x b)

= {[2(25 + 12) x 6] + (25 x 12)} m2

= (444 + 300) m2

= 744 m2.

Cost of plastering = Rs. 744 x 75 / 100 = Rs. 558
"

Q 8-The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A - 16 cm

B - 18 cm

C -24 cm

D - Data Inadeqaute

Answer - B

Explanation

"2(l+b)b 2(l+b)b = 5 2l + 2b = 5b 3b = 2l b = 23
 Then,
 Area = 216 cm2 
l x b = 216 l2 = 324 l = 18 cm.
"

Q 9-A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A - 2.91 m

B - 3 m

C - 5.82 m

D - None of these

Answer - B

Explanation

"Explanation: 
Area of the park = (60 x 40) m2= 2400 m2.

Area of the lawn = 2109 m2.

Area of the crossroads = (2400 - 2109) m2= 291 m2.

Let the width of the road be x metres. Then,

60x + 40x - x2 = 291

x2 - 100x + 291 = 0

(x - 97)(x - 3) = 0

x = 3.
"

Q 10-The diagonal of the floor of a rectangular closet is 7 1/2 feet. The shorter side of the closet is 4 1/2 feet. What is the area of the closet in square feet?

A - 51/4

B - 131/2

C - 27

D - 37

Answer - C

Explanation

"Other side = √1522−922 ft= √225/4−81/4ft
= √144/4ft= 6 ft  
Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.
"

Q 11-The ratio of the areas of two squares, one having double its diagonal then the other is:

A - 1 : 3

B - 3 : 1

C - 1 : 4

D - 4 : 1

Answer - D

Explanation

"Lenth of the diagonals be 2x and x units. 

 areas are 1/2 × (2x)2 and (1/2 × x2) 

 Required ratio = 1/2 × 4 x2 : 1/2 x2 = 4 : 1 "

Q 12-The length of a room is 6 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.

A - Rs. 25660

B - Rs. 25560

C - Rs. 25650

D - Rs. 26550

Answer - C

Explanation

"Area = 6 × 4.75 sq. metre.

 Cost for 1 sq. metre. = Rs. 900

 Hence total cost = 6 × 4.75 × 900 = 6 × 4275 = Rs. 25650 "

Q 13-A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?

A - 128 sq. ft.

B - 126 sq. ft.

C - 136 sq. ft.

D - 116 sq. ft.

Answer - A

Explanation

"Let l = 9 ft.

 Then l + 2b = 37

 => 2b = 37 - l = 37 - 9 = 28

 => b = 28/2 = 14 ft

 Area = lb = 9 × 14 = 126 sq. ft. "

Q 14-Of the two square fields, the area of the one is 1 hectare, while anothe one is broader by 1%. There differences in area is:

A - 200 m

B - 201 m

C - 202 m

D - None of these

Answer - B

Explanation

"Area of one square field = 10000 m2 

 10000 × 1 = 10000 

 Side of this field = √10000 m = 100 m 

 Side of another square = 101 m 

 Difference of areas = [ 1012 - 1002 ] m2 

 [101+100]-[101-100] m2

 (201) x (1) m2 = 201 m2 "

Q 15-A girl walking at the rate of 9 Km per hour crosses a square field diagonally in 12 seconds. The area of the field is:

A - 460 sq.m

B - 600 sq.m

C - 510 sq.m

D - 450 sq.m

Answer - D

Explanation

"Distance covered in (9×1000)/(3600) × 12 = 30 m 

 Diagonal of squarre field = 30 m. 

 area of square field = 302/2

 = 900/2 = 450 Sq.m "

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