Rhombus tiles

The floor of a building consists of 3000 rhombus-shaped tiles, and each of its diagonals is 45 cm and 30 cm in length. Find the cost of polishing the floor at the rate of $4 per square meter.

Correct answer:

x =  810 USD

Step-by-step explanation:

$$\begin{gathered} n=3000 \\ {d}_1=45\text{cm}\to \text{m}=45:100\text{m}=0.45\text{m} \\ {d}_2=30\text{cm}\to \text{m}=30:100\text{m}=0.3\text{m} \\ {S}_1=\frac{d_1\cdot d_2}{2}=\frac{0.45\cdot 0.3}{2}=\frac{27}{400}=0.0675{\text{m}}^2 \\ S=n\cdot S_1=3000\cdot 0.0675=\frac{405}{2}=202.5{\text{m}}^2 \\ c=4{\text{USD/m}}^2 \\ x=c\cdot S=4\cdot 202.5=810\text{USD} \end{gathered}$$

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