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Giải bài tập 7.18 trang 39 SGK Toán 9 tập 2 - Cùng khám phá

Bạn An sử dụng các hình viên phân như Hình 7.25a để ghép thành mẫu hoa văn trang trí như trong Hình 7.25b. Tính diện tích của mẫu hoa văn.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Bạn An sử dụng các hình viên phân như Hình 7.25a để ghép thành mẫu hoa văn trang trí như trong Hình 7.25b. Tính diện tích của mẫu hoa văn.

Phương pháp giải - Xem chi tiết

🦩Tính bán kính đường tròn ngoại tiếp của tam giác đều bằng \(\frac{{a\sqrt 3 }}{3}\).

♌Tính diện tích đường tròn ngoại tiếp của tam giác đều là S = \(\frac{\pi {a^2}}{3}\)

ಌTính diện tích tam giác đều \(\frac{{{a^2}\sqrt 3 }}{4}\) với cạnh a rồi lấy diện tích đường tròn trừ đi diện tích tam giác ta tìm được diện tích một viên phân.

Lời giải chi tiết

Ta có bán kính đường tròn ngoại tiếp của tam giác đều bằng \(\sqrt 3 \). Diện tích đường tròn ngoại tiếp của tam giác đều là:

S = \(\frac{\pi {3^2}}{3} = 3\pi \) cm2

Diện tích tam giác đều ABC là: \(\frac{{9\sqrt 3 }}{4}\) cm2

Diện tích 3 viên phân là:

\(3\pi  - \frac{{9\sqrt 3 }}{4} \approx 5,5\) cm2

Mà mẫu hoa văn tạo thành từ 6 viên phân nên có diện tích là:

2.5,5 \( \approx \) 11 cm2.

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