The area of a rhombus is given by half the product of the lengths of its diagonals, (1)/(2) × d_1 × d_2. Substituting d_1 = 45 cm and d_2 = 30 cm, we find the area of 1 tile to be 675 cm².

Since 1 m = 100 cm, we have 1 m² = 10000 cm². Dividing 2025000 by 10000 gives an area of 202.5 m².

The rate of polishing the floor is ₹ 4 per m². Multiplying the total area of 202.5 m² by ₹ 4 gives the total cost of ₹ 810.

the floor of a building consists to sauce 3000 tiles which are Rhombus shape and each of its diagonals of 45 cm and 30 cm in length find the total cost of pollution the floor if the cost per metre is rupees 4

Answer: ₹ 810

Step-by-step solution

Step 1: Find the area of one rhombus-shaped tile

The area of a rhombus is given by half the product of the lengths of its diagonals, $\frac{1}{2} \times d_1 \times d_2$ . Substituting $d_1 = 45\text{ cm}$ and $d_2 = 30\text{ cm}$ , we find the area of 1 tile to be $675\text{ cm}^2$ .

Step 2: Calculate the total area of the floor in square centimetres

The floor is made up of $3000$ identical tiles. Multiplying the area of 1 tile by $3000$ gives a total floor area of $2025000\text{ cm}^2$ .

Step 3: Convert the total floor area into square metres

Since $1\text{ m} = 100\text{ cm}$ , we have $1\text{ m}^2 = 10000\text{ cm}^2$ . Dividing $2025000$ by $10000$ gives an area of $202.5\text{ m}^2$ .

Step 4: Calculate the total cost of polishing the floor

The rate of polishing the floor is ₹ $4$ per $\text{m}^2$ . Multiplying the total area of $202.5\text{ m}^2$ by ₹ $4$ gives the total cost of ₹ $810$ .

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