Equilateral 26601

The gardener filled the flowerbed with crushed stone in the shape of an equilateral triangle with an 8-m-long side. If 25 kg of crumb was consumed per 1 m² of the area, how much crumb was used for the whole flower bed?

Correct answer:

m =  692.8203 kg

Step-by-step explanation:

$$\begin{gathered} a=8\text{m} \\ h=25{\text{kg/m}}^2 \\ S=\frac{\sqrt{3}}{4}\cdot a^2=\frac{\sqrt{3}}{4}\cdot 8^2=16\sqrt{3}{\text{m}}^2\doteq 27.7128{\text{m}}^2 \\ m=h\cdot S=25\cdot 27.7128=400\sqrt{3}=692.8203\text{kg} \end{gathered}$$

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