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Giải bài 9.12 trang 53 sách bài tập toán 9 - Kết nối tri thức tập 2

Tính chu vi và diện tích của tam giác đều ngoại tiếp một đường tròn bán kính 3cm.

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

Toán - Văn - Anh
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Đề bài

Tính chu vi và diện tích của tam giác đều ngoại tiếp một đường tròn bán kính 3cm.

Phương pháp giải - Xem chi tiết

+ Gọi h(cm), a(cm) lần lượt là chiều cao, cạnh của tam giác đều. Suy ra: \(\frac{1}{3}h = 3\), \(\frac{{\sqrt 3 }}{6}a = 3\), từ đó tìm được h và a. + Chu vi của tam giác đều là: \(C = 3a\). + Diện tích của tam giác đều là: \(S = \frac{1}{2}a.h\).

Lời giải chi tiết

Gọi h(cm), a(cm) lần lượt là chiều cao, cạnh của tam giác đều. Suy ra: \(\frac{1}{3}h = 3\). Do đó, \(h = 9cm\) Lại có: \(\frac{{\sqrt 3 }}{6}a = 3\) nên \(a = 6\sqrt 3 \left( {cm} \right)\). Chu vi của tam giác là: \(C = 3a = 18\sqrt 3 \left( {cm} \right)\). Diện tích của tam giác là: \(S = \frac{1}{2}a.h = 27\sqrt 3 \left( {c{m^2}} \right)\).

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

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