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Giải bài 6 trang 109 vở thực hành Toán 9 tập 2

Người ta muốn làm một khay đựng bánh kẹo hình lục giác đều có cạnh 10cm và chia thành 7 ngăn gồm một lục giác đều nhỏ và 6 hình thang cân như hình dưới đây. Hỏi lục giác đều nhỏ phải có cạnh bằng bao nhiêu để nó có diện tích bằng hai lần diện tích mỗi hình thang?

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

Toán - Văn - Anh
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Đề bài

Người ta muốn làm một khay đựng bánh kẹo hình lục giác đều có cạnh 10cm và chia thành 7 ngăn gồm một lục giác đều nhỏ và 6 hình thang cân như hình dưới đây. Hỏi lục giác đều nhỏ phải có cạnh bằng bao nhiêu để nó có diện tích bằng hai lần diện tích mỗi hình thang?

Phương pháp giải - Xem chi tiết

+ Nếu chia đôi lục giác đều nhỏ bởi một đường kính thì ra sẽ được hai hình thang cân nhỏ bằng nhau và bằng với các hình thang cân trước đó. + Do vậy đường kính của lục giác đều nhỏ phải bằng cạnh của lục giác đều lớn, từ đó tính được cạnh lục giác đều nhỏ.

Lời giải chi tiết

Nếu chia đôi lục giác đều nhỏ bởi một đường kính thì ra sẽ được hai hình thang cân nhỏ bằng nhau và bằng với các hình thang cân trước đó. Do vậy đường kính của lục giác đều nhỏ phải bằng cạnh của lục giác đều lớn, tức là bằng 10 cm. Vì vậy, cạnh lục giác đều nhỏ bằng \(\frac{1}{2}.10 = 5\) (cm).

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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