এই পোস্টে আমরা জানব ষষ্ঠ শ্রেনীর বিষয় গণিত এর ২য় অধ্যায়, দ্বিমাত্রিক বস্তুর গল্প সম্পর্কে।
প্রশ্নঃ কোণ কাকে বলে?
উত্তরঃ দুটি রেখাংশ পরস্পর কোন প্রান্তবিন্দুতে মিলিত হলে যে জ্যামিতিক আকার ধারণ করে তাকে কোণ বলে
প্রশ্নঃ সন্নিহিত কোণ কাকে বলে?
একই সমতলে অবস্থিত দুটি কোণের শীর্ষবিন্দু ও একটি রশ্মি যদি সাধারণ হয় এবং কোণ দুটি সাধারণ রশ্মি বিপরীত দিকে অবস্থান করে তবে কোণ দুটিকে পরস্পর সন্নিহিত কোণ বলে।
প্রশ্নঃ সমকোণ কাকে বলে?
উত্তরঃ দুইটি সরলরেখা যখন পরস্পরকে লম্বভাবে ছেদ করে তখন ছেদ বিন্দুতে যে কোণ উৎপন্ন হয় , তাই সমকোণ।
অন্যভাবে বলা যায়, যে কোণের পরিমান ৯০° ডিগ্রি তাকে সমকোণ বলা হয়।
অনুশীলনী
১) চিত্রে, AB = ১০০ সে.মি., AC = ১২০ সে.মি. এবং BD = ৮০ সে.মি. হলে CE=?
২) চিত্রে ABC ত্রিভুজের BD মধ্যমা এবং BC বাহুর দৈর্ঘ্য AD এর দ্বিগুণ।
ত্রিভুজটি কী ধরনের?
উত্তরের সপক্ষে যুক্তি দাও।
৩) একটি সমকোণী ত্রিভুজের বাহু তিনটি দৈর্ঘ্য ৫ সে.মি., ১২ সে.মি. এবং ১৩ সে.মি.।
ক) আনুপাতিক চিত্র অংকন করো।
খ) সমকৌণিক বিন্দু থেকে বিপ্রীত বাহুর অঙ্কিত দৈর্ঘ্য নির্ণয় করো।
সমাধানঃ
👉 সংখ্যার গল্প – সমাধান | গণিত – ১ম অধ্যায় | ষষ্ঠ শ্রেণী
পাজল
ক) শ্রেণিকক্ষের ছবিটি পূরণ করতে কতটি টাইলস প্রয়োজন হয়েছে?
খ) ছবিতে দেখানো শ্রেণিকক্ষ এবং একটি টাইলসের ক্ষেত্রফল নির্ণয় করে প্রয়োজনীয় টাইলসের সংখ্যা হিসাব করো। (সংকেত : AB ও ED রেখা সমান্তরাল। ABF ও BCF এর উচ্চতাগুলো এঁকে নিতে পার ।
গ) (ক) এবং (খ) থেকে প্রাপ্ত ফলাফলের মধ্যে পার্থক্য থাকলে তার যৌক্তিক ব্যাখ্যা দাও।
সমাধানঃ
ক) শ্রেণীকক্ষের ক্ষেত্রফল = ৩০ x ২০ বর্গ একক
= ৬০০ বর্গ একক
একটি টাইলসের ক্ষেত্রফল = ৭x৭ বর্গ একক
= ৪৯ বর্গ একক
শ্রেণীকক্ষে টাইলস প্রয়োজন = ৬০০ ÷ ৪৯ টি
= ১২.৪৪ টি .
খ) ছবিতে দেখানো EDCF আয়তক্ষেত্রে ক্ষেত্রফল = ৩০×২০ = ৬০০ বর্গএকক
একটি টাইলসের ক্ষেত্রফল = ৭×৭ = ৪৯ বর্গ একক
আবার, ABCF একটি ট্রাপিজিয়াম, সমান্তরাল দুই বাহুর দৈর্ঘ্য ৩০ একক ও ১৪ একক এবং উচ্চতা ২৮ – ২০ = ৮ একক
:. ক্ষেত্রফল = ১/২ × (সমান্তরাল বাহু দুটির যোগফল) × উচ্চতা
= ১/২ x (৩০ + ১৫) x ৮
= ৪৫ × ৪
= ১৮০
• EDCF + ABCF এর মোট ক্ষেত্রফল = ৬০০ + ১৮০
= ৭৮০ বর্গ একক
একটি টাইলসের ক্ষেত্রফল = ৭× ৭ = ৪৯ বর্গ একক
সম্পূর্ণ ছবিটি টাইলস দ্বারা পূরণ করতে টাইলস
প্রয়োজন = ৭৮০ ÷ ৪৯টি
= ১৫.৯২ টি (প্রায়)
গ) (ক) এবং (খ) থেকে প্রাপ্ত ফলাফলের পার্থক্য
ক্ষেত্রফলের পার্থক্য = (৭৮০ – ৬০০)
= ১৮০ বর্গ একক
টাইলসের সংখ্যার পার্থক্য = (১৫.৯২ – ১২.৪৪)
= ৩.৪৮ টি
ব্যাখ্যাঃ (ক) তে শুধু আয়তকার অংশের হিসাব করা হয়েছে
(খ) আয়তকার + ট্রাপিজিয়াম অংশের হিসাব করা হয়েছে।
সৃজনশীল
সমাধানঃ
১।
২। একটি আয়তাকার জমির ক্ষেত্রফল একটি বর্গাকার জমির ক্ষেত্রফলের সমান। আয়তাকার জমির দৈর্ঘ্য প্রস্থের ৪ গুণ। প্রতি মিটার দড়ির মূল্য ৭ টাকা। দড়ি দিয়ে দুইবার ঘুরিয়ে জমির চারদিকে বেষ্টনি দিতে মোট ৫৬০০ টাকা খরচ হয়।
ক) আয়তাকার জমির পরিসীমা কত হবে?
খ) বর্গাকার জমিতে প্রতি ৪ বর্গমিটার জায়গায় একটি করে পেঁপের চারা রোপন করলে কতটি চারা লাগবে?
৩। চিত্রের সামান্তরিক ক্ষেত্রটির পরিসীমা ১৮০ মিটার এবং এর ক্ষেত্রফল একাধিক উপায়ে নির্ণয় করা যায়।
ক) সামান্তরিক ক্ষেত্রটির ক্ষেত্রফল যৌক্তিক ব্যাখ্যাসহ একাধিক পদ্ধতিতে নির্ণয় করো।
খ) দেখাও যে, সামান্তরিক ক্ষেত্রটির ক্ষেত্রফল = ত্রিভুজক্ষেত্র ABD এর দ্বিগুণ।
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৪) একটি ঘরের মেঝে ২৬ মিটার লম্বা ও ২০ মিটার চওড়া। ৪ মি. লম্বা ও ২.৫ মি. চওড়া কয়টি মাদুর দিয়ে মেঝেটি সম্পূর্ণ ঢাকা যাবে? প্রতিটি মাদুরের দাম ৪৫ টাকা হলে, মোট খরচ কত হবে?
সমাধান:
দেওয়া আছে, ঘরের মেঝের দৈর্ঘ্য = ২৬ মিটার, চওড়া প্রস্থ = ২০ মিটার।
ঘরের মেঝের ক্ষেত্রফল = (২৬ × ২০) বর্গমিটার
= ৫২০ বর্গমিটার
দেওয়া আছে, মাদুরের লম্বা বা দৈর্ঘ্য =৪ মিটার, চওড়া বা প্রস্থ = ২.৫ মিটার
ঘরের মেঝের ক্ষেত্রফল = (৪ x ২.৫) বর্গমিটার
= ১০ বর্গমিটার
মেঝেটি সম্পূর্ণ ঢাকতে মাদুর প্রয়োজন (৫২০ ÷ ১০)টি = ৫২টি
একটি মাদুরের দাম ৪৫টাকা হলে, ৫২টি মাদুরের দাম = (৫২ x ৪৫) টাকা = ১৩৪০ টাকা।
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