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’ is 24.
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Answer 1

Given

• Floor of 3000 tiles
• Rhombus of Diagonals are 45cm and 30cm
• Rate of Polishing = 24 /m²

Explanation

Firstly We've to find the area of a tile and area of whole Floor tiles as:-

$\maltese {\pmb{\boxed{\sf{ Area_{(Rhombus)} = \dfrac{1}{2} \times d_1 \times d_2 }}}} \\ \\ \\ \colon\implies{\sf{ Area_{(3000 \ tiles)} = \dfrac{1}{ \cancel{2} } \times 45 \times \cancel{30} \times 3000 }} \\ \\ \\ \colon\implies{\sf{ Area_{(3000 \ tiles)} = 45 \times 15 \times 3000 }} \\ \\ \\ \colon\implies{\sf\green{ Area_{(3000 \ tiles)} = 2025000 \ cm^2 }}$

So, Area of 3000 such tiles will be 2025000 cm².

Now, We have to convert this area into m² by Dividing from 10000 as:-

10000 cm² = 1 m²

$\colon\mapsto{\sf{ m^2 = \dfrac{2025000}{10000} }} \\ \\ \colon\mapsto{\sf{ m^2 = 202.5 }}$

So, Area of 3000 such tiles will be 202.5 m².

Now, we can find the cost of Polishing the Floor at the rate of ₹24 per m² as:-

$\colon\implies{\sf{ 202.5 \times 24 }} \\ \\ \colon\implies{\pmb{\sf{ Rs. \ 4860}}}$

Hence,

${\underline{\sf{ The \ Total \ cost \ of \ Polishing }}} \\ {\underline{\sf{ the \ Floor \ is \ Rs. \ 4860. }}}$