# SSC > Mensuration

Explore popular questions from Mensuration for SSC. This collection covers Mensuration previous year SSC questions hand picked by experienced teachers.

General Intelligence and Reasoning
General Awareness
Quantitative Aptitude
English Comprehension
Q 1.

Correct4

Incorrect-1

If the length of the diagonal AC of a square ABCD is {tex} 5.2 \mathrm { cm } , {/tex} then the area of the square is :

A

15.12 sq.cm

13.52 sq.cm

C

12.62 sq.cm

D

{tex} 10.00 \mathrm { sq.cm } {/tex}

##### Explanation

Q 2.

Correct4

Incorrect-1

The length of the diagonal of a square is 'a'cm. Which of the following represents the area of the square (in sq. {tex} \mathrm { cm } . ) ? {/tex}

A

{tex} 2 a {/tex}

B

{tex} \frac { a } { \sqrt { 2 } } {/tex}

{tex} \mathrm { a } ^ { 2 } / 2 {/tex}

D

{tex} a ^ { 2 } / 4 {/tex}

##### Explanation

Q 3.

Correct4

Incorrect-1

The diagonal of a square is {tex} 4 \sqrt { 2 } {/tex} {tex} \mathrm { cm } . {/tex} The diagonal of another square whose area is double that of the first square is :

A

{tex} 8 \sqrt { 2 } \mathrm { cm } {/tex}

B

{tex} 16 \mathrm { cm } {/tex}

C

{tex} \sqrt { 32 } \mathrm { cm } {/tex}

{tex} 8 \mathrm { cm } {/tex}

##### Explanation

Q 4.

Correct4

Incorrect-1

The diagonal of a square {tex} A {/tex} is {tex} ( a + b ) . {/tex} The diagonal of a square whose area is twice the area of square {tex} \mathrm { A } , {/tex} is

A

{tex} 2 ( a + b ) {/tex}

B

{tex} 2 ( a + b ) ^ { 2 } {/tex}

{tex} \sqrt { 2 } ( a + b ) {/tex}

D

{tex} \sqrt { 2 } ( a - b ) {/tex}

##### Explanation

Q 5.

Correct4

Incorrect-1

The difference of the areas of two squares drawn on two line segments of different lengths is {tex} 32 \mathrm { sq\ .cm } {/tex}. Find the length of the greater line segment if one is longer than the other by {tex} 2 \mathrm { cm } . {/tex}

A

{tex} 7 \mathrm { cm } {/tex}

{tex} 9 \mathrm { cm } {/tex}

C

{tex} 11 \mathrm { cm } {/tex}

D

{tex} 16 \mathrm { cm } {/tex}

##### Explanation

Q 6.

Correct4

Incorrect-1

If the diagonals of two squares are in the ratio of {tex} 2: 5 , {/tex} their area will be in the ratio of

A

{tex} \sqrt { 2 }: \sqrt { 5 } {/tex}

B

{tex}2:5{/tex}

{tex}4:25{/tex}

D

{tex}4:5{/tex}

##### Explanation

Q 7.

Correct4

Incorrect-1

The perimeter of five squares are {tex} 24 \mathrm { cm } , 32 \mathrm { cm } , 40 \mathrm { cm } , 76 \mathrm { cm } {/tex} and {tex} 80 \mathrm { cm } {/tex} respectively. The perimeter of another square equal in area to sum of the areas of these squares is :

A

{tex} 31 \mathrm { cm } {/tex}

B

{tex} 62 \mathrm { cm } {/tex}

{tex} 124 \mathrm { cm } {/tex}

D

{tex} 961 \mathrm { cm } {/tex}

##### Explanation

Q 8.

Correct4

Incorrect-1

The ratio of the area of a square to that of the square drawn on its diagonal is :

A

1:1

1:2

C

1:3

D

1:4

##### Explanation

Q 9.

Correct4

Incorrect-1

From four corners of a square sheet of side {tex} 4 \mathrm { cm } , {/tex} four pieces, each in the shape of are of a circle with radius {tex} 2 \mathrm { cm } , {/tex} are cut out. The area of the remaining portion is :

A

{tex} ( 8 - \pi ) {/tex} sq.cm.

{tex} ( 16 - 4 \pi ) \mathrm { sq.cm } {/tex}

C

{tex} ( 16 - 8 \pi ) {/tex} sq.cm.

D

{tex} ( 4 - 2 \pi ) \mathrm { sq.cm } {/tex}

##### Explanation

Q 10.

Correct4

Incorrect-1

The length of diagonal of a square is {tex} 15 \sqrt { 2 } \mathrm { cm } . {/tex} Its area is

A

{tex} 112.5 \mathrm { cm } ^ { 2 } {/tex}

B

{tex} 450 \mathrm { cm } ^ { 2 } {/tex}

C

{tex} \frac { 225 \sqrt { 2 } } { 2 } \mathrm { cm } ^ { 2 } {/tex}

{tex} 225 \mathrm { cm } ^ { 2 } {/tex}

##### Explanation

Q 11.

Correct4

Incorrect-1

A kite in the shape of a square with a diagonal {tex} 32 \mathrm { cm } {/tex} attached to an equilateral triangle of the base {tex} 8 \mathrm { cm } {/tex}. Approximately how much paper has been used to make it? (Use {tex} \sqrt { 3 } = 1.732 ) {/tex}

{tex} 539.712 \mathrm { cm } ^ { 2 } {/tex}

B

{tex} 538.721 \mathrm { cm } ^ { 2 } {/tex}

C

{tex} 540.712 \mathrm { cm } ^ { 2 } {/tex}

D

{tex} 539.217 \mathrm { cm } ^ { 2 } {/tex}

##### Explanation

Q 12.

Correct4

Incorrect-1

The breadth of a rectangular hall is three-fourth of its length. If the area of the floor is 768 sq. {tex} \mathrm { m } {/tex}. then the difference between the length and breadth of the hall is:

8 metres

B

12 metres

C

24 metres

D

32 metres

##### Explanation

Q 13.

Correct4

Incorrect-1

The length of a plot is five times its breadth. A playground measuring 245 square metres occupies half of the total area of the plot. What is the length of the plot?

{tex} 35 \sqrt { 2 } {/tex} metres

B

{tex} 175 \sqrt { 2 } {/tex} metres

C

{tex}490{/tex} metres

D

{tex} 5 \sqrt { 2 } {/tex} metres

##### Explanation

Q 14.

Correct4

Incorrect-1

The length of a rectangular garden is 12 metres and its breadth is 5 metres. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden :

{tex} 2 \sqrt { 30 } \mathrm { m } {/tex}

B

{tex} \sqrt { 13 } \mathrm { m } {/tex}

C

{tex} 13 \mathrm { m } {/tex}

D

{tex} 8 \sqrt { 15 } \mathrm { m } {/tex}

##### Explanation

Q 15.

Correct4

Incorrect-1

A circular wire of diameter {tex} 42 \mathrm { cm } {/tex} is folded in the shape of a rectangle whose sides are in the ratio 6: 5 . Find the area enclosed by the rectangle. (Take {tex} \left. \pi = \frac { 22 } { 7 } \right) {/tex}

A

{tex} 540 \mathrm { cm } ^ { 2 } {/tex}

{tex} 1080 \mathrm { cm } ^ { 2 } {/tex}

C

{tex} 2160 \mathrm { cm } ^ { 2 } {/tex}

D

{tex} 4320 \mathrm { cm } ^ { 2 } {/tex}

##### Explanation

Q 16.

Correct4

Incorrect-1

A took {tex}15{/tex} sec. to cross a rectangular field diagonally walking at the rate of {tex} 52 \mathrm { m } / \mathrm { min } {/tex}. and {tex} \mathrm { B } {/tex} took the same time to cross the same field along its sides walking at the rate of {tex} 68 \mathrm { m } / {/tex} min. The area of the field is:

A

{tex} 30 \mathrm { m } ^ { 2 } {/tex}

B

{tex} 40 \mathrm { m } ^ { 2 } {/tex}

C

{tex} 50 \mathrm { m } ^ { 2 } {/tex}

{tex} 60 \mathrm { m } ^ { 2 } {/tex}

##### Explanation

Q 17.

Correct4

Incorrect-1

The difference between the length and breadth of a rectangle is {tex}23 \mathrm { m } {/tex}. If its perimeter is {tex} 206 \mathrm { m } , {/tex} then its area is

A

{tex} 1520 \mathrm { m } ^ { 2 } {/tex}

B

{tex} 2420 \mathrm { m } ^ { 2 } {/tex}

C

{tex} 2480 \mathrm { m } ^ { 2 } {/tex}

{tex} 2520 \mathrm { m } ^ { 2 } {/tex}

##### Explanation

Q 18.

Correct4

Incorrect-1

There is a rectangular tank of length {tex} 180 \mathrm { m } {/tex} and breadth {tex} 120 \mathrm { m } {/tex} in a circular field. If the area of the land portion of the field is {tex} 40000 \mathrm { m } ^ { 2 } , {/tex} what is the radius of
the field {tex} ? {/tex} (Take {tex} \pi = \frac { 22 } { 7 } {/tex} )

A

{tex} 130 \mathrm { m } {/tex}

B

{tex} 135 \mathrm { m } {/tex}

{tex} 140 \mathrm { m } {/tex}

D

{tex} 145 \mathrm { m } {/tex}

##### Explanation

Q 19.

Correct4

Incorrect-1

The length of a rectangular hall is {tex} 5 \mathrm { m } {/tex} more than its breadth. The area of the hall is {tex} 750 \mathrm { m } ^ { 2 } . {/tex} The length of the hall is :

A

{tex} 15 \mathrm { m } {/tex}

B

{tex} 22.5 \mathrm { m } {/tex}

C

{tex} 25 \mathrm { m } {/tex}

{tex} 30 \mathrm { m } {/tex}

##### Explanation

Q 20.

Correct4

Incorrect-1

If the length and breadth of a rectangle are in the ratio {tex} 3: 2{/tex} and its perimeter is {tex} 20 \mathrm { cm } {/tex}, then the area of the rectangle ( {tex} \mathrm { i } \mathrm { n } {/tex}, {tex} \mathrm { cm } ^ { 2 } {/tex} ) is :

24

B

48

C

72

D

96

##### Explanation

Q 21.

Correct4

Incorrect-1

A path of uniform width runs round the inside of a rectangular field {tex} 38 \mathrm { m } {/tex} long and {tex} 32 \mathrm { m } {/tex} wide. If the path occupies {tex} 600 \mathrm { m } ^ { 2 } {/tex}, then the width of the path is

A

{tex} 30 \mathrm { m } {/tex}

{tex} 5 \mathrm { m } {/tex}

C

{tex} 18.75 \mathrm { m } {/tex}

D

{tex} 10 \mathrm { m } {/tex}

##### Explanation

Q 22.

Correct4

Incorrect-1

The length and breadth of a rectangle are increased by {tex} 20 \% {/tex} and {tex} 25 \% {/tex} respectively. The increase in the area of the resulting rectangle will be :

A

{tex} 60 \% {/tex}

{tex} 50 \% {/tex}

C

{tex} 40 \% {/tex}

D

{tex} 30 \% {/tex}

##### Explanation

Q 23.

Correct4

Incorrect-1

The length of a room floor exceeds its breadth by {tex} 20 \mathrm { m } {/tex}. The area of the floor remains unaltered when the length is decreased by {tex} 10 \mathrm { m } {/tex} but the breadth is increased by {tex} 5 \mathrm { m } {/tex}. The area of the floor (in square metres) is:

A

280

B

325

300

D

420

##### Explanation

Q 24.

Correct4

Incorrect-1

A street of width {tex} 10{/tex} metres surrounds from outside a rectangular garden whose measurement is {tex} 200 \mathrm { m } \times 180 \mathrm { m } {/tex}. The area of the path (in square metres) is

8000

B

7000

C

7500

D

8200

##### Explanation

Q 25.

Correct4

Incorrect-1

In measuring the sides of a rectangle, there is an excess of {tex} 5 \% {/tex} on one side and {tex} 2 \% {/tex} deficit on the other. Then the error percent in the area is

A

{tex} 3 \cdot 3 \% {/tex}

B

{tex} 3 \cdot 0 \% {/tex}

{tex} 2 \cdot 9 \% {/tex}

D

{tex} 2 \cdot 7 \% {/tex}