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Bài 8.19 trang 72 SGK Toán 11 tập 2 - Cùng khám phá

Cho hình chóp cụt tứ giác đều ABCD.A’B’C’D’, cạnh đáy lớn bằng \(5\sqrt 2 a\)
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Đề bài

Cho hình chóp cụt tứ giác đều ABCD.A’B’C’D’, cạnh đáy lớn bằng \(5\sqrt 2 a\), cạnh đáy nhỏ bằng \(2\sqrt 2 a\) và chiều cao bằng 4a. Tỉnh độ dài cạnh bên của hình chóp cụt đều này.

Phương pháp giải - Xem chi tiết

Kẻ D’H, C’G vuông góc với CD. Tính DH. Áp dụng Py-ta-go để tính DD’.

Lời giải chi tiết

Kẻ D’H, C’G vuông góc với CD nên D’H song song với C’GMà C’D’ song song với HGSuy ra D’C’GH là hình chữ nhật nên HG = \(2\sqrt 2 a\)\( \Rightarrow DH + CG = 3\sqrt 2 a \Rightarrow DH = CG = \frac{{3\sqrt 2 }}{2}a\)Xét tam giác D’HD vuông tại H có:\(DD' = \sqrt {D'{H^2} + D{H^2}}  = \sqrt {{{\left( {4a} \right)}^2} + {{\left( {\frac{{3\sqrt 2 }}{2}a} \right)}^2}}  = \frac{{41}}{2}a\)

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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