#### Question

The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m^{2} is Rs 4.

#### Solution

Given:

The floor consist of 3000 rhombus shaped tiles .

The lengths of the diagonals of each tile are 45 cm and 30 cm.

∴Area of a rhombus shaped tile =\[ \frac{1}{2} \times (45 \times 30) = 675 {cm}^2 \]

∴ Area of the complete floor\[ = 3000 \times 675 = 2025000 {cm}^2 \]

Now, we need to convert this area into `m^2` because the rate of polishing is given as per `m^2`.

\[ \therefore 2025000 {cm}^2 = 2025000 \times cm \times cm\]

\[ = 2025000 \times \frac{1}{100} m \times \frac{1}{100} m\]

\[ = 202 . 5 m^2 \]

Now, the cost of polishing 1 `m^2` is Rs 4.

∴ Total cost of polishing the complete floor = 202 . 5 x 4 = 810

Thus, the total cost of polishing the floor is Rs 810.