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Giải bài 10.20 trang 123 SGK Toán 8 tập 2 - Kết nối tri thức

Tính diện tích xung quanh của hình chóp tam giác đều,

🉐Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

🍷Tính diện tích xung quanh của hình chóp tam giác đều, hình chóp tứ giác đều trong Hình 10.36

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Quan sát hình 10.36: xác định các kích thước và  áp dụng công thức tính diện tích xung quanh của hình chóp tam giác, tứ giác đều để tính.

Lời giải chi tiết

* Nửa chu vi của tam giác ABC là:

\(\left( {12 + 12 + 12} \right):2 = 18 \)

Xét tam giác HBD vuông tại H, có:

🤡\(\begin{array}{l}H{{\rm{D}}^2} = B{{\rm{D}}^2} - B{H^2} = {8^2} - {6^2}\\ \Rightarrow H{\rm{D}} = 2\sqrt 7 \end{array}\)

Diện tích xung quanh của hình chóp tam giác đều là:

\({S_{xq}} = p.d = 18.2\sqrt 7  = 36\sqrt 7  \)

* Nủa chu vi của tứ giác ABCD là:

\(\left( {10.4} \right):2 = 20\)

Xét tam giác SHD vuông tại H, ta có:

🌄\(\begin{array}{l}S{H^2} = S{{\rm{D}}^2} - H{{\rm{D}}^2} = {12^2} - {6^2} = 119\\ \Rightarrow SH = \sqrt {119} \end{array}\)

Diện tích xung quanh của hình chóp tứ giác đều là:

🍬\({S_{xq}} = p.d = 20.\sqrt {119}  = 20\sqrt {119}  \)

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