Diamond tile paving

How many diamond-shaped tiles with a side of 25 cm and a height of 20 cm are needed to pave a rectangular courtyard with sides of 30 m and 28 m if the joints represent 1/20 of the area?

Final Answer:

n =  15960

Step-by-step explanation:

$$\begin{gathered} a=30\text{m} \\ b=28\text{m} \\ {S}_1=a\cdot b=30\cdot 28=840{\text{m}}^2 \\ {S}_2=S_1-S_1/20=840-840/20=798{\text{m}}^2 \\ {S}_3=S_2\to {\text{cm}}^2=S_2\cdot 10000{\text{cm}}^2=798\cdot 10000{\text{cm}}^2=7980000{\text{cm}}^2 \\ x=25\text{cm} \\ y=20\text{cm} \\ {S}_4=x\cdot y=25\cdot 20=500{\text{cm}}^2 \\ n=S_3/S_4=7980000/500=15960 \end{gathered}$$

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