Mensuration Test

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Mensuration Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

Area of one swimming pool which is in rectangular shape is half of the area of another swimming pool which is in square shape. If the area of squared shape swimming pool is 64 m², what would be the breadth of the rectangular shaped swimming pool, provided length of the side of square pool is same as length of rectangular pool?

A
2 m

B
4 m

C
5 m

D
7 m

Solution

It is given that,
(Area of rectangular pool) = (Area of square pool)
(Length x breadth) = × 64 m².
Area of square pool = 64 m²So area of rectangular pool = 32 m²Side of square = 8 m
Also length of rectangle = length of side of square = 8 m
(8 x Breadth) = 32

Breadth = = 4 m
Question 2
1 / -0

The figure below shows the blue print of a hotel. If the area of each square is 10 cm², what is the area of the hotel in the blueprint?

A
110 cm²

B
100 cm²

C
90 cm²

D
80 cm²

Solution

Area of 1 square = 10 cm²
Number of squares = 11

So, the area of given figure is 110 cm²
Question 3
1 / -0

The shape of a garden is rectangular and the area of the garden is 24 m². Which of the following may not be the possible dimensions of the rectangular garden?

A
Length - 8 m, breadth - 4 m

B
Length - 6 m, breadth - 4 m

C
Length - 12 m, breadth - 2 m.

D
Length - 8 m, breadth - 3 m.

Solution

As Area = L x B
So 8 x 4 = 32 m² cannot be a possibility.
Question 4
1 / -0

Find the area of the given figure.

A
240 m²

B
230 m²

C
232 m²

D
236 m²

Solution

Area of square ABCD = side x side = 4 × 4 = 16 m²Area of rectangle CEFG = length × breadth = 16 × 4 = 64 m²Area of rectangle HIKJ = 16 × 4 = 64 m²Area of rectangle NKML = 12 × 8 = 96 m²Total area of this figure is = 16 + 64 + 64 + 96 = 240 m²
Question 5
1 / -0

A roof of a house measures 80 m by 40.2 m. Find the perimeter of the roof.

A
24400 cm

B
25000 cm

C
19800 cm

D
22200 cm

Solution

Breadth of roof = 40 m 200 cm

=> 4000 cm + 200 cm = 4200 cm (1 m = 100 cm)

Length = 8000 cm

Perimeter = 2(8000 cm + 4200 cm) = 24400 cm
Question 6
1 / -0

Find the perimeter of the shaded region in the given figure.

A
18 units

B
16 units

C
20 units

D
22 units

Solution

Perimeter of the shaded region is
(18 x 1) units = 18 units
Question 7
1 / -0

Find the perimeter of the given figure.

A
50 cm

B
54 cm

C
60 cm

D
62 cm

Solution

Perimeter of the given figure = 10 + 6 + 1 + 10 + 12 + 10 + 1 = 50 cm
Question 8
1 / -0

The breadth of a rectangle is ()^th of its length. If its area is 4 m², then what will be its perimeter?

A
10 m

B
14 m

C
16 m

D
26 m

Solution

Breadth = x Length
Area = length x breadth
4 = length x length
(length)² = 16

Length = 4 m

Breadth = 1 m

Perimeter = 2( length + breadth)

= 2(4 + 1)

= 10 m
Question 9
1 / -0

A teacher asked his students to draw a triangle. Ali drew an equilateral triangle and the perimeter of that triangle was 24 cm. Find the length of triangle.

A
8 cm

B
12 cm

C
10 cm

D
3 cm

Solution

Given perimeter = 24 cm

3 x length = 24 cm

Length = 8 cm
Question 10
1 / -0

Which of the following figures has the smallest perimeter if each side of the square is 1 unit?

A
A

B
B

C
D

D
C

Solution

Perimeter of A = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10 units

Perimeter of B = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 14 units

Perimeter of C = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 14 units

Perimeter of D = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 14 units

So, figure A is the correct option.
Question 11
1 / -0

If side of a square is doubled, then the area of the square becomes ____________ times the original area.

A
2

B

C
4

D
7

Solution

Let side of square be x.

Area = x²

If side is doubled = 2x

New area = (2x)² = 4x²

Therefore, the new area is 4 times the original area.
Question 12
1 / -0

A square park has an area of 3600 m² . What will be the value of 6 times its perimeter?

A
980 m

B
1100 m

C
1440 m

D
1650 m

Solution

Area of square = 3600 m²

Side of square = = 60 m

Perimeter = 4 x 60 = 240 m

6 times perimeter = 6 x 240 = 1440 m
Question 13
1 / -0

What is the missing length in the given figure?

A
6 m

B
9 m

C
10 m

D
12 m

Solution

Perimeter of quadrilateral = sum of all sides
26 m = 8 m + 5 m + 4 m + ?
? = 26 - 5 - 4 - 8 = 9 m
Question 14
1 / -0

Area of a square is numerically double than its perimeter. What is the length of its side, if the area is 400 cm²?

A
55 cm

B
50 cm

C
45 cm

D
40 cm

Solution

Let side be x.

Perimeter = 4x

According to question,

400 = 2 x perimeter

400 = 8 x

x = 50 cm
Question 15
1 / -0

A figure is formed by putting 3 rectangles one over the other as shown in figure. If length and breadth of each rectangle is 5 m and 4 m respectively, what is the perimeter of this figure?

A
18 m

B
22 m

C
34 m

D
46 m

Solution

Perimeter = [(4 + 4 + 4) + 5] x 2 = 34 m
Question 16
1 / -0

There are 96 square tiles which make up the floor of the hall in a wedding palace. If the perimeter of each tile is 8 m, what is the area of the floor of the hall?

A
356 m²

B
372 m²

C
384 m²

D
392 m²

Solution

Perimeter of each square tile = side × number of sides
8 = side × 4
8 ÷ 4 = side
side = 2 m
Area of each tile = side²
= 2²
= 4 m²
Area of 96 tiles on the floor = 4 × 96
= 384 m²
Question 17
1 / -0

How much length of a ribbon is required to cover the sides of a photograph of size 51.75 cm x 41 cm?

A
170.75 cm

B
178 cm

C
185.5 cm

D
193.25 cm

Solution

Perimeter of the picture = 2 (51.75 cm + 41 cm)

= 2 X 92.75 = 185.5 cm

So 185.5 cm of ribbon is required.
Question 18
1 / -0

A swimming pool of area 1176 m² has length of 42 m. What is the breadth of this pool?

A
23 m

B
28 m

C
34 m

D
39 m

Solution

Area = length X breadth
1176 = 42 X breadth
Breadth = 1176 ÷ 42 = 28 m
Question 19
1 / -0

Find the number of tiles needed to cover a plot with length and breadth as 4.45 m and 3.20 m, respectively, if the size of one tile is 20 cm by 20 cm.

A
335

B
356

C
377

D
401

Solution

Area of plot = 4.45 × 3.20 m²
or 445 × 320 cm²= 1,42,400 cm²Area of tile = 20 × 20 = 400 cm²
Number of tiles = 142400 ÷ 400 = 356
Question 20
1 / -0

How many paper slips of size 36 cm by 24 cm can be cut from a big sheet of paper of size 360 cm by 84 cm?

A
24

B
29

C
35

D
42

Solution

Area of big sheet = 360 X 84 = 30,240 cm²
Area of paper slip = 36 X 24 = 864 cm²
Number of slips that can be cut = 30240÷864 = 35
Question 21
1 / -0

Ali walks four times around a rectangular field of length 5 m and breadth 8 m. Benny walks thrice around a square field of side 15 m. Who covered more distance and by how much?

A
Benny, 76 m

B
Benny, 56 m

C
Ali, 56 m

D
Ali, 76 m

Solution

Perimeter of rectangular field = 2(l + b) = 2(5 + 8) = 2 x 13 = 26 m
Distance Ali walked = 4 times the perimeter of rectangular field = 4 x 26 = 104 m
Perimeter of square field = 4 (side) = 4 x 15 = 60 m
Distance Benny walked = 3 times the perimeter of square field = 3 x 60 = 180 m
Difference = 180 - 104 = 76 m
So, Benny covered more distance than Ali by 76 m.
Question 22
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Deny wants to put a fence around his garden of length 12 m and breadth 15 m. Find the total cost of fencing at the rate of Rs. 20 per metre.

A
Rs. 900

B
Rs. 970

C
Rs. 1030

D
Rs. 1080

Solution

Perimeter of garden = 2(l + b) = 2(12 + 15) = 54 m
Cost of fencing per metre = Rs. 20
Cost of fencing 54 metres = 54 × 20 = Rs. 1080
Question 23
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A rectangular pool of length 6 m and width 5 m is embedded with 6 square tiles of side 2 m on some part of the pool. Calculate the area of the remaining part?

A
4 m²

B
5 m²

C
6 m²

D
7 m²

Solution

Area of the pool =
Area = =
Area of one square tile =
Area = =
Area of 6 tiles = =

Difference = 30 - 24 =
Question 24
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What is the distance covered by John, if he walks 30 rounds of a park of equilateral triangle shape of side 18 m?

A
1620 m

B
1650 m

C
1670 m

D
1700 m

Solution

Length of each side of a park = 18 m
Perimeter of the given park = 3 x 18 = 54 m
Distance covered by John in rounds = 30 x 54 = 1620 m
Question 25
1 / -0

Usain Bolt takes 50 rounds of square park of side 25 m. What is the total distance covered by him?

A
5000 m

B
1000 m

C
4000 m

D
2000 m

Solution

Side of a square park = 25 m
Perimeter of the park = sum of all sides = 25 + 25 + 25 + 25 = 100 m
So the total distance travelled by Usain Bolt in 50 rounds = 50 x 100 = 5000 m
Question 26
1 / -0

Which of following figures has the minimum shaded area?

A
A

B
C

C
B

D
All have the same area

Solution

Figure (A)
Area = (10 x 2) + (8 x 2)
= 20 + 16
= 36 sq. m

Figure (B)
Area = (7 x 2) + (7 x 2) + (4 x 2)
= 14 + 14 + 8
= 36 sq. m

Figure (C)
Area = (8 x 7) - (6 x 5)
= 56 - 30
= 26 sq. m

So we can say that Figure (C) has minimum shaded area.
Question 27
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State 'T' for true and F for false.

(i) Area of square is side squared.

(ii) Pentagon has six sides.

(iii) Distance covered along the boundary of a closed figure is called perimeter.

A
(i) T (ii) F (iii) T

B
(i) T (ii) F (iii) F

C
(i) F (ii) F (iii) T

D
(i) F (ii) T (iii) F

Solution

(i) True: the area of square is side squared , that is A =
(ii) False: as pentagon has 5 sides
(iii) True: Distance covered along the boundary of a closed figure is called perimeter.
Question 28
1 / -0

Find the area of given figure if all the circles are equal to each other having radius 4 cm.

A
200.96 sq. cm

B
214.23 sq. cm

C
220.12 sq. cm

D
225.25 sq. cm

Solution

Radius of circles = 4 cm
Area of 1 circle = π x r²
= 3.14 x 4 x 4
= 50.24 sq. cm
Area of whole figure= 50.24 x 4 = 200.96 sq. cm

Question 29

1 / -0

Find the values of P, Q, R and S

Length of rectangle Cm	Breadth of rectangle Cm	Area Cm²	Perimetor Cm
12	P	144	Q
R	24	S	68

(P) 132 cm, (Q) 48 cm, (R) 10 cm, (S) 240 cm²

(P) 12 cm, (Q) 48 cm, (R) 20 cm, (S) 240 cm²

(P) 12 cm, (Q) 48 cm, (R) 10 cm, (S) 240 cm²

(P) 12 cm, (Q) 24 cm, (R) 10 cm, (S) 240 cm²

Solution

(P) 12 cm, as 12 x 12 = 144 cm²
(Q) 48 cm, sum of all sides = 2 x (12 + 12) = 48 cm
(R)10 cm
Perimeter = 68 = 2 x ( x + 24)
68 - 48 = 2x
20 = 2x
x = 10
(S) 240 cm², area of rectangle = l x b = 10 x 24 = 240 cm²

Question 30
1 / -0

Figure A is made up of 8 identical squares. Three squares are removed from figure A to get figure B. If the perimeter of figure B is 320 cm. What is the perimeter of figure A?

A
420 cm

B
580 cm

C
480 cm

D
512 cm

Solution

Let each side be x.
Perimeter of each square = 4x
Perimeter of figure B = 5 4x = 320
x = 16 cm
Perimeter of figure A = 8 x 4x = 8 x 4 x 16 = 512 cm

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Mensuration Test - 10

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Mensuration Test - 10

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SHARING IS CARING

Question 1

2 m

4 m

5 m

7 m

Solution

Question 2

110 cm2

100 cm2

90 cm2

80 cm2

Solution

Question 3

Length - 8 m, breadth - 4 m

Length - 6 m, breadth - 4 m

Length - 12 m, breadth - 2 m.

Length - 8 m, breadth - 3 m.

Solution

Question 4

240 m2

230 m2

232 m2

236 m2

Solution

Question 5

24400 cm

25000 cm

19800 cm

22200 cm

Solution

Question 6

18 units

16 units

20 units

22 units

Solution

Question 7

50 cm

54 cm

60 cm

62 cm

Solution

Question 8

10 m

14 m

16 m

26 m

Solution

Question 9

8 cm

12 cm

10 cm

3 cm

Solution

Question 10

A

B

D

C

Solution

Question 11

2

4

7

Solution

Question 12

980 m

1100 m

1440 m

1650 m

Solution

Question 13

110 cm²

100 cm²

90 cm²

80 cm²

240 m²

230 m²

232 m²

236 m²

356 m²

372 m²

384 m²

392 m²

4 m²

5 m²

6 m²

7 m²