Question
Download Solution PDFট্রাপিজিয়াম ABCD-তে, ∠BAE = 30°, ∠CDF = 45°, BC = 6 সেমি এবং AB = 12 সেমি হয়। ABCD এর ক্ষেত্রফল নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFΔABE-তে,
⇒ cos30° = AE/AB
⇒ AE = 6√3 সেমি
⇒ sin30° = BE/AB
⇒ BE = 6 সেমি
ΔCFD-তে,
⇒ tan45° = CF/FD
⇒ FD = 6 সেমি [∵ BE = CF = 6 সেমি]
⇒ AD = AE + EF + FD
⇒ AD = 6√3 + 6 + 6 সেমি
⇒ AD = 12 + 6√3 সেমি
⇒ ট্র্যাপিজিয়ামের ক্ষেত্রফল = 1/2 x (সমান্তরাল বাহুর সমষ্টি) x উচ্চতা
⇒ ট্র্যাপিজিয়ামের ক্ষেত্রফল = 1/2 x (BC + AD) x BE
∴ ট্র্যাপিজিয়ামের ক্ষেত্রফল = 1/2 x (12 + 6√3 + 6) x 6 = 18(3 + √3) সেমি2
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