Answer :

Total area covered by the roads = 441 m²

The total cost of constructing the roads at the RATE of Rs 110 per m² = Rs. 48,510

Given :

• Length of the rectangular field = 90 m
• Breadth of the rectangular field = 60 m
• Two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields
• Width of each road = 3 m

To find :

• The area covered by the roads
• The cost of constructing the roads at the rate of Rs. 110 per m²

Solution :

Firstly, we will calculate the area of first road :-

Using formula,

★ Area of the road = l × b

where,

• l denotes length of the road
• b denotes breadth of the road

we have,

• l = 90 m
• b = 3 m

Substituting the given values,

→ Area of the first road = 90 × 3

→ Area of the first road = 270

• Area of the first road = 270 m²

Now, calculate the area of the second road :-

Using formula,

★ Area of the road = l × b

we have,

• l = 60 m
• b = 3 m

Substituting the given values,

→ Area of the second road = 60 × 3

→ Area of the second road = 180

• Area of the second road = 180 m²

The roads have a common portion in the centre of the rectangular field which is sqaure in shape.

So, we will calculate the area of that portion and subtract it from any one of the area.

Using formula,

★ Area of square = side²

we have,

• side = 3 m

Substituting the given value,

→Area of the common portion = (3)²

→ Area of the common portion = 9

Area of the common portion which is square in shape = 9 m²

Now, subtracting it from any one area of the road.

→ Area = 180 - 9

→ Area = 171

Area of the second road = 171 m²

Now, add both the areas of the road, the resultant value will be the total area covered by the roads.

→ Total area covered by the roads = Area of first road + Area of second road

→ Total area = 270 + 171

→ Total area = 441

Total area covered by the roads = 441 m²

Cost of constructing the roads :-

Cost of constructing 1 m² of the road = Rs. 110

Cost of constructing 441 m² of the road = 441 × 110 = 48,510

The total cost of constructing the roads at the rate of Rs 110 per m² = Rs. 48,510