Question

The floor of a building consists of around 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of flooring if each tile costs rupees 20 per ${{m}^{2}}$.

Answer 1

Hint: Here, first of all we will find the area of each tile. Then we will multiply the number of tiles with the area of one tile to get the total area. After that we will multiply the cost of 1 ${{m}^{2}}$ to get the total cost.

Complete step-by-step answer:
Since, each of the tiles is in the form of rhombus. So, we will use the formula of area of a rhombus which is given as:

$Area=\dfrac{1}{2}\times {{d}_{1}}\times {{d}_{2}}$, where ${{d}_{1}}$ and ${{d}_{2}}$ are the length of the diagonals.

  It is given that the lengths of the diagonals are 45 cm and 30 cm.

Therefore, are of each rhombus is:

$=\dfrac{1}{2}\times 45\times 30=675c{{m}^{2}}$

Now, the total number of tiles is = 3000

So, we will apply the unitary method to find the total area of 3000 tiles.

So, area of 3000 tiles =$3000\times 675=202500\,c{{m}^{2}}$

Now, we can convert the unit as:

Since, 1 cm = 0.01 m

So, $1\,c{{m}^{2}}=\left( 0.01 \right){{m}^{2}}$

On converting the total area into ${{m}^{2}}$, we get:

Total area of tiles =$2025000\times 0.01\times 0.01\,{{m}^{2}}$

Since, cost for a area of $1\,{{m}^{2}}$ is = Rs. 20

So, total cost for the area of $202.5\,{{m}^{2}}$ is =$Rs.\,202.5\times 20=Rs.4,050$

Hence, the cost of flooring is Rs.4,050.

Note: It should be noted that the conversion of area of tiles from $c{{m}^{2}}\,\,to\,\,{{m}^{2}}$ is necessary because the cost is given in per ${{m}^{2}}$. The formula for the area of rhombus must be remembered by the student.