• Mensuration (Class - VI)
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Mensuration (Class - VI)

Description: Mensuration
Number of Questions: 18
Created by:
Tags: Mensuration Calculating the Area of Square Objects Calculating the Perimeter of Rectangle Area and Its Meaning
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The cost of fencing a rectangular park of length 175 m is Rs. 7200. If the rate of fencing is Rs. 12 per metre, then find the breadth of the park.

  1. 250 m

  2. 150 m

  3. 75 m

  4. 125 m

  5. -

Show answer
Correct Option: D
Explanation:

This is the correct answer. The total cost of fencing is Rs. 7200. The rate of fencing is Rs. 12/m.

Perimeter x rate of fencing = total cost Perimeter = total cost/rate = 7200/12 = 600 m Length = 175  Breadth = ? Perimeter = 600 P = 2(L + B) 600 = 2(175 + b) = 350 + 2b 600 - 350 = 2b 250 = 2b b = 250/2 = 125 m

The sides of a rectangle are in the ratio 5 : 4. If the perimeter of the rectangle is 72 cm, then find its length.

  1. 40 cm

  2. 20 cm

  3. 16 cm

  4. 63 cm

  5. -

Show answer
Correct Option: B
Explanation:

This is the correct answer. Let the length be 5x. And let the breadth be 4x. Perimeter = 2(L + B) 72 = 2(5x + 4x) 9x = 36 x = 36/9 x = 4 Therefore, length = 5 x 4 = 20 cm Breadth = 4 x 4 = 16 cm

If a plane region R is divided into n squares, with each side measuring 1 cm, then the area of the region R is

  1. n cm

  2. n2 cm

  3. n2 cm2

  4. n cm2

  5. -

Show answer
Correct Option: D
Explanation:

This is the correct answer. Area of one square of side 1 cm = 1 cm2 So, area of n squares = n x 1 cm2 = n cm2

A marble tile measures 25 cm by 20 cm. How many such tiles will be required to cover a wall of size 4 m and 3 m?

  1. 240

  2. 41

  3. 230

  4. 40

  5. -

Show answer
Correct Option: A
Explanation:

This is the correct answer. For the wall, L = 4 m = 400 cm, B = 3 m = 300 cm Area of the wall = 400 x 300 = 120000 cm2
For a marble tile, L = 25 cm, B = 20 cm Area = 25 x 20 = 500 cm2 Number of tiles = Area of the wall/Area of a tile = 120000/500 = 240

The area of a square is 256 cm2. Find its side.

  1. 128 cm

  2. 16 cm

  3. 8 cm

  4. 126 cm

  5. -

Show answer
Correct Option: B
Explanation:

This is the correct answer. Area of square = Side x Side 256 = Side x Side Factors of 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 Side x Side = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 Side = 2 x 2 x 2 x 2 = 16 cm

An athlete runs around a square field of side 32 cm. If he takes three rounds of the field, find the total distance covered by him.

  1. 3072 cm

  2. 384 cm

  3. 348 cm

  4. 3082 cm

  5. -

Show answer
Correct Option: B
Explanation:

This is the correct answer. Side of the square field = 32 cm Perimeter of the field = 4 x 32 = 128 cm He takes three rounds, so total distance covered = 128 X 3 = 384 cm

Find the perimeter of a hexagon with each side measuring 8 cm.

  1. 48 cm

  2. 40 cm

  3. 56 cm

  4. 32 cm

  5. -

Show answer
Correct Option: A
Explanation:

This is the correct answer. A hexagon has 6 sides. Perimeter = 6 x side = 6 x 8 = 48 cm

The perimeter of an isosceles triangle, whose base measures 12 cm, is 32 cm. Find the measures of the other two sides of the triangle.

  1. 20 cm, 20 cm

  2. 10 cm, 10 cm

  3. 5 cm, 5 cm

  4. 15 cm, 15 cm

  5. -

Show answer
Correct Option: B
Explanation:

This is the correct answer. An isosceles triangle has two sides equal. Perimeter of the triangle = 2x + 12 32 = 2x + 32 2x = 32 - 12 = 20 x = 20/2 = 10 cm Other side = 10 cm

What will happen to the area of a rectangle if its length and breadth are doubled?

  1. It will be doubled.

  2. It will remain the same.

  3. It will be increased four times.

  4. It will be increased three times.

  5. -

Show answer
Correct Option: C
Explanation:

This is the correct answer. If the length and breadth of a rectangle are doubled, then Area = 2l X 2b = 4lb

The total cost of flooring a room at Rs. 8.50 per square metre is Rs. 1700. If the length of the room is 16 cm, find its breadth.

  1. 20 cm

  2. 12.5 cm

  3. 900 cm

  4. 15.2 cm

  5. -

Show answer
Correct Option: B
Explanation:

This is the correct answer. Total cost of flooring = Rs. 1700 Rate of flooring = Rs. 8.50 per m2 Area of the floor = Total cost/Rate per square metre = 1700/8.50 = 200 m2 Breadth of the room = Area/Length = 200/16 = 12.5 cm

The area of a rectangle of breadth 17 cm is 340 cm2. Find the perimeter of the rectangle.

  1. 74 cm

  2. 54 cm

  3. 78 cm

  4. 58 cm

  5. -

Show answer
Correct Option: A
Explanation:

This is the correct answer. Length of the rectangle = Area/Breadth = 340/17 = 20 cm Perimeter = 2(l + b) = 2(17 + 20) = 2 x 37 = 74 cm

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

  1. 225 : 256

  2. 60 : 64

  3. 24 : 26

  4. 15 : 16

  5. -

Show answer
Correct Option: D
Explanation:

This is the correct answer. Let the side of square 1 be s1 and that of square 2 be s2. So, the ratio of their areas is (s1)2 : (s2)2 = 225 : 256 (s1)2 : (s2)2 = (15)2 : (16)2 So, s1 = 15, s2 = 16 So, the ratio is 15 : 16. The ratio of their perimeters is 4 x 15 : 4 x 16 = 60 : 64 = 15 : 16.

Find the breadth of a rectangle whose perimeter is 360 cm and length is 1 m.

  1. 180 cm

  2. 36 cm

  3. 80 cm

  4. 179 cm

  5. -

Show answer
Correct Option: C
Explanation:

This is the correct answer. Length of the rectangle, l = 1 m = 100 cm P = 2(l + b) l = P/2 - b = (360/2) - 100 = 180 - 100 = 80 cm

The perimeter of a regular pentagon is 120 cm. How long is its each side?

  1. 30 cm

  2. 24 cm

  3. 15 cm

  4. 40 cm

  5. -

Show answer
Correct Option: B
Explanation:

This is the correct answer. A pentagon has 5 sides. Side = perimeter/5 = 120/5 = 24 cm

Find the perimeter of a square plot whose side is 22.5 cm.

  1. 506.25 cm

  2. 560.25 cm

  3. 90 cm

  4. 80 cm

  5. -

Show answer
Correct Option: C
Explanation:

This is the correct answer. Perimeter = 4 x side = 4 X 22.5 = 90 cm

The dimensions of a picture are 30 cm x 20 cm. What is the length of a wooden frame needed to frame the picture?

  1. 100 cm

  2. 600 cm

  3. 50 cm

  4. 120 cm

  5. -

Show answer
Correct Option: A
Explanation:

This is the correct answer. The length of the wooden frame is the perimeter of the picture. L = 30 cm, B = 20 cm Perimeter = 2(L + B) = 2(30 + 20) = 2 X 50 = 100 cm The length of the wooden frame is 100 cm.

If the side of a square is tripled, what will happen to its area?

  1. It will increase 4 times.

  2. It will increase 6 times.

  3. It will increase 9 times.

  4. It will increase 12 times.

  5. -

Show answer
Correct Option: C
Explanation:

This is the correct answer. If the side of the square is tripled, new side = 3x Area = (3x) X 3x = 9x2 The area will be increased 9 times.

One side of a square plot is 2.5 m. Find the cost of levelling it at a rate of Rs. 2 per square metre.

  1. Rs. 12.5

  2. Rs. 15.2

  3. Rs. 125

  4. Rs. 152

  5. -

Show answer
Correct Option: A
Explanation:

This is the correct answer. Area of the square plot = 2.5 x 2.5 = 6.25 m2 Cost of levelling = Area x rate per metre = 6.25 x 2 = Rs. 12.5

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