Equilateral 81770

Calculate the area of the circle in which the hole is cut in the shape of an equilateral triangle when the diameter of the circle, d=32mm, and the side of the triangle, a=20.8mm.

Correct answer:

S =  616.9091 mm²

Step-by-step explanation:

$$\begin{gathered} d=32\text{mm} \\ a=20.8\text{mm} \\ {S}_1=\pi \cdot (d/2{)}^2=3.1416\cdot (32/2{)}^2\doteq 804.2477{\text{mm}}^2 \\ {S}_2=\frac{\sqrt{3}}{4}\cdot a^2=\frac{\sqrt{3}}{4}\cdot 20.8^2\doteq 187.3386{\text{mm}}^2 \\ S=S_1-S_2=804.2477-187.3386=616.9091{\text{mm}}^2 \end{gathered}$$

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