Mensuration(6th Grade > Mathematics ) Questions and answers for exam Preparation

Question 1. Given the area of a circle is 36 cm². The area of the rectangle is

\frac{1}{6}

^th of the area of the circle. If the breadth of the rectangle is 1 cm, what is the length?

6 cm
12 cm
36 cm
26 cm

Explanation:-

Answer: Option A. -> 6 cm
:
A
Given, Area of circle = 36 cm²
Area of rectangle =

\frac{Area of circle}{6}

....(given)
=

\frac{36}{6}

= 6 cm²

∵

Area of rectangle =length x breadth

\Rightarrow

6 =length x 1
So, length = 6 cm

Question 2. Find the cost of ploughing a rectangular farm at the rate of ₹ 12/m² , having length equal to 12 m and width equal to 5 m.

₹ 120
₹ 720
₹ 360
₹ 240

Explanation:-

Answer: Option B. -> ₹ 720
:
B
Area of rectangular field
= length

\times

breadth
= 12

\times

5
=

60 m^{2}

Cost of ploughing
= Total area

\times

cost per sq. metre
=

60 \times 12

= ₹720

Question 3. Which of the following options correctly describes the given figure?

It is a regular figure.
It is closed.
Number of sides can be found out.
It is an open figure.

Explanation:-

Answer: Option B. -> It is closed.
:
B
Given figure is an irregular figure, for which the number of sides cannot be found out. The figure is also a closed one.

Question 4. How many sides we have to cover in order to make a complete round of the given figure?

4
14
12
10

Explanation:-

Answer: Option C. -> 12
:
C
The given figure has atotal of 12 sides (AB, BC, CD, DE, EF, FG, GH, HI, IJ, JK, KL and LA). In order to complete a full round, one should reach the same corner one started from. So, wehaveto cover12 sides.

Question 5. Find the area of a rectangle whose length is 4 cm and its breadth is 3 cm. [1 MARK]

Explanation:-

:
Solution: 1 Mark
Area of the rectangle = length

\times

breadth

= 4 \times 3

= 12 {c m}^{2}

Question 6. Prashant wants to cover his kitchen shelf with square tiles of side 0.5 m. The kitchen shelf's dimensions being 4m by 3m. Find the number of tiles required. If each tile costs Rs 70, how much will he have to spend for covering his kitchen shelf? [4 MARKS]

Explanation:-

:
Steps: 2 Marks
Formula: 1 Mark
Answer: 1 Mark
Area of one square tile = (side)

^{2}

= (0.5m)

^{2}

= 0.25 m

^{2} .

Area of the kitchen shelf = length

\times

breadth
= 4

\times

3 = 12m
Number of tiles
=

\frac{Area of kitchen shelf}{Area of square tile}

=

\frac{12}{0.25}

= 48
Cost of 1 tile = Rs70
Cost of 48 tiles = Rs 48

\times

70 = Rs 3360

Question 7. How many sides a pentagon have? Shakshi was playing in a park which was shaped as a pentagon. Each side of the Pentagon was 30 m. She took one complete round on its boundary. What is the distance covered by her? [3 MARKS]

Explanation:-

:
Pentagon: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Pentagon has 5 sides.

How Many Sides A Pentagon Have? Shakshi Was Playing In A Pa...

Given that each side of the pentagon

= 30 m

The perimeter of a regular pentagon
=

5 \times

length of each side
=

5 \times 30

=

150 m

Hence, the distance covered by Shakshi is

150 m .

Question 8. Find the perimeter of the following figure. [3 MARKS]

Explanation:-

:
Steps: 2 Marks
Answer: 1 Mark

Perimeter of thefigure will be:
= 3 cm + 6 cm + 3 cm + 3 cm + 10 cm + 3 cm + 2 cm + 3 cm + 2 cm + 3 cm
(Starting from the topmost edge and going clockwise)

= 38 c m

Question 9. The area of a square field is

576 m^{2}

. Find [4 MARKS]
(i) The length of its sides
(ii) The length of its perimeter
(iii) Cost of fixing a fence along the boundary of the field at the rate of Rs 3.20 per metre.

Explanation:-

:
Steps: 2 Marks
Formula: 1 Mark
Answer: 1 Mark
(i) Let

l

be the length of the square

\Rightarrow

Area of square =

l^{2}

\Rightarrow l^{2} = 576

\Rightarrow l = 24 m

(ii)Perimeter of square = 4l

\Rightarrow 4 \times (24) = 96 m

(iii) Cost of fixing a fence

= ₹ (96 \times 3.20) = ₹ 307.20

Question 10. A rectangle has a length of 10 inches and breadth of 5 inches. The perimeter of the rectangle will be

30 square inches
30 inches
15 square inches
15 inches

Explanation:-

Answer: Option B. -> 30 inches
:
B
Perimeter of a rectangle
= 2

\times

(Length + Breadth)
=2

\times

( 10 inches + 5 inches )
= 30 inches.