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3 years ago

Express answer in exact form. Show all work for full credit.

Mathematics

1 answer:

Gennadij [26K]3 years ago

4 0

Answer:

Area segment = 3/2 π - (9/4)√3 units²

Step-by-step explanation:

∵ The hexagon is regular, then it is formed by 6 equilateral Δ

∵ Area segment = area sector - area Δ

∵ Area sector = (Ф/360) × πr²

∵ Ф = 60° ⇒ central angle of the sector

∵ r = 3

∴ Area sector = (60/360) × (3)² × π = 3/2 π

∵ Area equilateral Δ = 1/4 s²√3

∵ The length of the side of the Δ = 3

∴ Area Δ = 1/4 × (3)² √3 = (9/4)√3

∴ Area segment = 3/2 π - (9/4)√3 units²

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