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SSC Quantitative Aptitude - Area Important Questions

Quantitative Aptitude - Area

Exam Duration: 45 Mins Total Questions : 30

1 )

The perimeter of a rhombus is 56 m and its height is 5 m. Its area is:

(a)
64 sq. m
(b)
70 sq. m
(c)
78 sq. m
(d)
84 sq. m

2 )

A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?

(a)
55
(b)
56
(c)
57
(d)
58

3 )

The two parallel sides of a trapezium are 1.5 m and 2.5 m respectively. if the perpendicular distance between them is 6.5 meters, the area of the trapezium is:

(a)
10 m²
(b)
13 m²
(c)
20 m²
(d)
26 m²

4 )

A cow is tethered in the middle of a field of with a 14 feet long rope.If the cow grazes 100 sq. ft. per day, then approximately what time will be taken by the cow to graze the whole field?

(a)
2 days
(b)
6 days
(c)
24 days
(d)
None of these

5 )

Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has larger area and by how much?

(a)
Both have equal area
(b)
Square,33 cm²
(c)
Circle, 33 cm²
(d)
Square, 495 cm²

6 )

The areas of two circular fields are in the ratio 16:49. If the radius of the latter is 14m, then what is the radius of the former?

(a)
4 m
(b)
8 m
(c)
18 m
(d)
32 m

7 )

A semi-circular shaped window has diameter of 63 cm. Its perimeter equals:

(a)
126 cm
(b)
162 cm
(c)
198 cm
(d)
251 cm

8 )

The area of the largest circle, that can be drawn inside a rectangle with sides 18 cm by 14 cm is:

(a)
49 cm²
(b)
154 cm²
(c)
378 cm²
(d)
1078 cm²

9 )

The area of a circle is 220 sq. cm. The area of a square inscribed in this circle will be:

(a)
49 cm²
(b)
70 cm²
(c)
140 cm²
(d)
150 cm²

10 )

The radius of the circumcircle of an equilateral triangle of side 12 cm is:

(a)
\(\frac { 4\sqrt { 2 } }{ 3 } \)cm
(b)
\(4\sqrt { 2 } \) cm
(c)
\(\frac { 4\sqrt { 3 } }{ 3 } \) cm
(d)
\(4\sqrt { 3 } \) cm

11 )

Four circular cardboard pieces, each of radius 7 cm area placed in such a way that each piece touches two other pieces. The area of the space enclosed by the four pieces is:

(a)
21 cm²
(b)
42 cm²
(c)
84 cm²
(d)
168 cm²

12 )

The question given below consists of a statement and /or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and
Area of a square is equal to the area of a circle. What is the circumference of the circle?

I. The diagonal of the square is x inches.

II. The side of the sqUare is y inches.

(a)
if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;
(b)
if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question;
(c)
if the data either in Statement I or in Statement II alone are sufficient to answer the question;
(d)
if the data even in both Statements I and II together are not sufficient to answer the question;
(e)
if the data in both Statements I and II together are necessary to answer the question;

13 )

The area of a rectangle is eq1ual to the area of a circle. What is the length of the rectangle?

I. The radius of the circle is equal to the breadth of the rectangle.

II. The perimeter of the rectangle is 14 cm more than that of the circle.

(a)
if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;
(b)
if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question;
(c)
if the data either in Statement I or in Statement II alone are sufficient to answer the question;
(d)
if the data even in both Statements I and II together are not sufficient to answer the question;
(e)
if the data in both Statements I and II together are necessary to answer the question;

14 )

What is the height of the triangle?

I. The area of the triangle is 20 times its base.

II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.

(a)
if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;
(b)
if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question;
(c)
if the data either in Statement I or in Statement II alone are sufficient to answer the question;
(d)
if the data even in both Statements I and II together are not sufficient to answer the question;
(e)
if the data in both Statements I and II together are necessary to answer the question;

15 )

If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq.m. If the length is increased by 1 m and breadth is decreased by 1 m, then the area is decreased by 5 sq.m. The perimeter of the floor is:

(a)
30 m
(b)
32 m
(c)
36 m
(d)
40 m

16 )

The number of marble slabs of size 20 cm X 30 cm required to pave the floor of a square room of side 3 metres, is:

(a)
100
(b)
150
(c)
225
(d)
250

17 )

The perimeter of a square is 48 cm. The area of a rectangle is 4 cm² less than the area of the square. If the length of the rectangle is 14 cm, then its perimeter is:

(a)
24 cm
(b)
48 cm
(c)
50 cm
(d)
54 cm

18 )

If the perimeter of a rectangle and a square, each is equal to 80 cm and the difference of their areas is 100 sq.cm, the sides of the rectangle are:

(a)
25 cm, 15 cm
(b)
28 cm, 12 cm
(c)
30 cm, 10 cm
(d)
35 cm, 15 cm

19 )

The area of a square field is 69696 cm². Its diagonal will be equal to:

(a)
313.296 m
(b)
353.296 m
(c)
373.296 m
(d)
393.296 m

20 )

If the perimeters of a square and a rectangle are the same, then the area A and B enclosed by them would satisfy the condition:

(a)
A
(b)
A\(\le\)B
(c)
A>B
(d)
A\(\ge\)B

21 )

If the ratio of areas of two squares is 225:256, then the ratio of their perimeters is:

(a)
225 : 256
(b)
256 : 225
(c)
15 : 16
(d)
16 : 15

22 )

If the diagonal of a square is made 1.5 times, then the ratio of the areas of two squares is:

(a)
4 :3
(b)
4 :5
(c)
4 :7
(d)
4: 9

23 )

The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by:

(a)
35%
(b)
42%
(c)
62%
(d)
82%

24 )

The dimensions of a room are 10 m x 7 m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3 m. One window is of size 2 m x 1.5 m and the other two windows are of size 1m x 1.5 m. The cost of painting the walls at Rs. 3 per m² is:

(a)
Rs. 474
(b)
Rs. 578.50
(c)
Rs. 684
(d)
Rs. 894

25 )

The cost of papering the four walls of a room is Rs. 475. Each one of the length, breadth and height of another room is double that of this room. The cost of papering the walls of this new room is:

(a)
Rs. 712.50
(b)
Rs. 950
(c)
Rs. 1425
(d)
Rs. 1900

26 )

The ratio of height of a room to its semiperimeter is 2:5. It costs Rs.260 to paper the walls of the room with paper 50 cm wide at Rs. 2 per metre allowing an area of 15 sq.m for doors and windows. The height of the room is:

(a)
2.6 m
(b)
3.9 m
(c)
4 m
(d)
4.2 m

27 )

The base of a triangle is 15 cm and height is 12 cm. The height of another triangle of double the area having the base 20 cm is:

(a)
8 cm
(b)
9 cm
(c)
12.5 cm
(d)
18 cm

28 )

The area of a triangle is 216 cm² and its sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is:

(a)
6 cm
(b)
12 cm
(c)
36 cm
(d)
72 cm

29 )

The perimeter of a triangle is 30 cm and its area is 30 cm². If the largest side measures 13 cm, then what is the length of the smallest side of the triangle?