Pyramid planting

The flower bed has the shape of a regular 4-sided pyramid. The edge of the lower plinth is 10 m, and the upper plinth is 9 m. The deviation of the side wall from the base is 45 degrees. How many plantings should be purchased if 90 are needed to plant 1 square meter?

Final Answer:

n =  2420

Step-by-step explanation:

$$\begin{gathered} a=10 \\ b=9 \\ k=2\cdot \cos (45°\to \text{rad})=2\cdot \cos (45°\cdot \frac{\pi }{180})=2\cdot \cos (45°\cdot \frac{3.1415926}{180})=1.41421 \\ {h}_1=a/k=10/1.4142=5\sqrt{2}\doteq 7.0711 \\ {h}_2=b/k=9/1.4142\doteq 6.364 \\ {S}_1=a\cdot h_1/2=10\cdot 7.0711/2=25\sqrt{2}\doteq 35.3553 \\ {S}_2=b\cdot h_2/2=9\cdot 6.364/2\doteq 28.6378 \\ S=S_1-S_2=35.3553-28.6378\doteq 6.7175 \\ n=4\cdot \lceil 90\cdot S\rceil =4\cdot \lceil 90\cdot 6.7175\rceil =2420 \end{gathered}$$

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