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SSC > Mensuration

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

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}

Explanation