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Giải bài 5 trang 112 vở thực hành Toán 8 tập 2

Cho hình chóp tam giác đều S.ABC có các cạnh bên bằng 10cm, cạnh đáy bằng 12 cm. (H.10.7). Tính diện tích xung quanh của hình chóp tam giác đều S.ABC.

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Đề bài

Cho hình chóp tam giác đều S.ABC có các cạnh bên bằng 10cm, cạnh đáy bằng 12 cm. (H.10.7). Tính diện tích xung quanh của hình chóp tam giác đều S.ABC.

Phương pháp giải - Xem chi tiết

Áp dụng định lí Pythagore để tính độ dài trung đoạn. Sau đó sử dụng công thức tính diện tích xung quanh của hình chóp tam giác để tính diện tích xung quanh của hình chóp tam giác đều S.ABC.

Lời giải chi tiết

AH = 6cm. \(\Delta SAH\) vuông tại H nên theo định lí Pythagore ta có SH2 + AH2 = SA2.

SH2 + 622 = 102

SH2 = 102 – 62 = 82

Suy ra SH = 8 (cm)Diện tích xung quanh của hình chóp là: \({S_{xq}} = p.d = \frac{{12.3}}{2}.8 = 144\left( {c{m^2}} \right)\).

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