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Hình viên phân là gì? Cách tính diện tích hình viên phân - Toán 9

1. Khái niệm hình viên phân

Hình viên phân là hình giới hạn bởi một cung tròn và dây cung (tương ứng) của đường tròn (minh hoạ bởi phần tô đậm.

2. Cách tính diện tích hình viên phân

Để tính diện tích hình viên phân trong hình vẽ, ta làm như sau: + Tính diện tích tam giác OAB: $S=\frac{1}{2}.$ chiều cao. đáy tương ứng. + Tính diện tích hình quạt tròn: $S=\frac{\pi {{R}^{2}}n}{360}$ + Diện tích hình viên phân = diện tích hình quạt tròn – diện tích hình tam giác.

3. Cách tính diện tích hình quạt tròn

Diện tích ${{S}_{q}}$ của hình quạt tròn bán kính R ứng với cung $n{}^\circ $:

${{S}_{q}}=\frac{n}{360}\pi {{R}^{2}}=\frac{l.R}{2}$

Ví dụ: Diện tích hình quạt tròn có độ dài tương ứng với nó là $l=4\pi $cm, bán kính là R = 5cm là:

${{S}_{q}}=\frac{l.R}{2}=\frac{4\pi .5}{2}=10\pi \left( c{{m}^{2}} \right)$

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