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Question: Puja is the owner of a farm as shown in the figure. She goes to the market to buy the fence wire for the field. Calculate the minimum length of the wire to be bought by Puja so that the entire farm is covered. (All dimensions are in m) 

Options:
A.55 m
B.70 m
C.60 m
D.45 m
Answer: Option B
: B

To find out theminimum length of the wire to be bought by Puja so that the entire farm is covered, we have to find out the perimeter of the entire farm. From the above figure, the length of the side AF = (Length of side BC) - (Length of side ED) = (20-5) m = 15m.
Length of side AB = (Length of side DC + Length of side FE) = (5+10) m = 15m As we know, the perimeter of a plane figure is the length of its boundary. Perimeter of the farm = (15+20+5+5+10+15) m = 70 m. So, the minimum length of the wire to be bought by Puja is 70 m.

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Question 1. Raj runs and covers a distance of 0.616 km in   the ground which is in the shape  of semi-circle mounted on the rectangle as shown below. Find the number of rounds taken by Raj to cover the distance 




___

: Perimeter of half circle = πr + d .
But according to the figure given here ,
the perimeter of the part of the semi circle = π×142=7π=7×227=22m. (Radius is half the diameter)

Hence, total perimeter = Perimeter of the half circle + side of 14 m + side of 10 m + side of 10 m

= (22 + 14 + 10 +10) m = 56 m.

Number of rounds he will have to make to complete the punishment = 0.616×1000m56m = 11 rounds.
Question 2. There is a square park in the society. The management wants to put a circular fountain at the centre of the park with diameter 14 m. The remaining area is to be covered with grass. If the cost of laying grass is  20 per m2 and the cost of constructing the fountain is 10 per m2 . Find the length of the field if the total cost incurred is 6460 .( Use π = 22/7)




___

: Diameter of a circular fountain= 14 m, so radius = 7 m. Let the length of the square be 'a'. Total cost = cost of fountain + cost of grass. Hence, 6460 = (area of fountain x cost per m2) + (area of square park -area of circular fountain) x (cost for grass per m2) 6460 = (π(7)2×10)+((a2π(7)2×20) 6460 = (154×10)+(a2154)×20 6460 =1540+(a2154)×20 a = 20 m.
Question 3. Find the base length of a parallelogram if the area is 24 m2  and the corresponding height is 8 m.
  1.    3 m
  2.    4 m
  3.    5 m
  4.    1 m
Answer: Option A
: A

Area of a parallelogram = Base × corresponding height ​.

Therefore, Base = Area of a parallelogramCorresponding height

Base = 248= 3 m.
Question 4. One hectare = ________m2. (Enter a numeric value)


___

: Thehectare(symbolha) is anSIacceptedmetric systemunit ofareaequal a square with 100-metre sides(10,000 m2) and primarily used in the measurement of land.
Hence, 1 hectare = 10000m2.

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