Question

The floor of a building consists of 3000 tiles which are rhombus shape and each of its diagonals is 45cm and 30cm in length. Find the total cost of polishing the floor, if the cost per sq. meter is Rs.4.

Answer 1

Hint: First, find the area of the rhombus using the formula , $A = \dfrac{1}{2}\left( {{d_1} \times {d_2}} \right)$, where ${d_1}$ and ${d_2}$ are the length of the diagonals of the rhombus. Next, multiply it with 3000 to find the total area of the floor. Convert the area into ${m^2}$ and then multiply it by 4 to find the total cost.

Complete step by step solution: The shape of the tile is of a rhombus.
The lengths of the diagonals of a rhombus are 45cm and 30cm.
We know that the area of the rhombus is half the product of its diagonals.
That is, $A = \dfrac{1}{2}\left( {{d_1} \times {d_2}} \right)$, where ${d_1}$ and ${d_2}$ are the length of the diagonals of the rhombus.
On substituting the values of the length of the diagonals as 45cm and 30cm, we will have
$A = \dfrac{1}{2}\left( {45 \times 30} \right)$
On solving the above equation, we will get,
$
  A = \left( {45 \times 15} \right) \\
  A = 675c{m^2} \\
$
Now, we are given that there are 3000 tiles, then the area of all the tiles is the product of the area of one tile and the total number of tiles.
That is,
$675 \times 3000 = 20,25,000c{m^2}$
We are given that cost of polishing is Rs. 4 per square metre.
Therefore, we will first convert the area of tiles from $c{m^2}$ to ${m^2}$ by dividing the area by 10,000
Hence, the area of the tiles is $\dfrac{{20,25,000}}{{10,000}} = 202.5{m^2}$
Now, multiply the area of the tiles with 4 to find the total cost of polishing.
$202.5 \times 4 = 810$

Hence, the total cost of polishing the floor is Rs. 108.

Note: From the students perspective we need to remember the formula to solve a mensuration problem. There can be many variations for this question. Instead of rhombus shape tiles, it can be the triangular shape or square shape tiles. we need to use the formula accordingly.