It's swimming time!

Geometry Level 3

A regular hexagon swimming pool has a side length of 3 3 meters. It is surrounded by a sidewalk of uniform width 1.2 1.2 meters. The sidewalk is surrounded by a grass landscape of uniform width 0.4 0.4 meters.

Which of the following is the combined area of the sidewalk and landscape?

144 5 + 128 25 3 \dfrac{144}{5}+\dfrac{128}{25}\sqrt{3} 24 5 5 + 64 75 3 \dfrac{24}{5}\sqrt{5}+\dfrac{64}{75}\sqrt{3} 6 ( 16 15 3 + 3 ) 6\left(\dfrac{16}{15}\sqrt{3}+3\right) 3 ( 144 5 2 + 128 25 ) \sqrt{3}\left(\dfrac{144}{5}\sqrt{2}+\dfrac{128}{25}\right)

A Former Brilliant Member by A Former Brilliant Member

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