চতুর্ভুজ (Quadrilateral) (৮.১)

অষ্টম শ্রেণি (মাধ্যমিক ২০২৫) - গণিত চতুৰ্ভুজ | - | NCTB BOOK
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চারটি রেখাংশ দ্বারা আবদ্ধ চিত্র একটি চতুর্ভুজ। চিত্র দ্বারা আবদ্ধ ক্ষেত্রটি একটি চতুর্ভুজক্ষেত্র।

চতুর্ভুজের চারটি বাহু আছে। যে চারটি রেখাংশ দ্বারা ক্ষেত্রটি আবদ্ধ হয়, এ চারটি রেখাংশই চতুর্ভুজের বাহু।

A, B, C ও D বিন্দু চারটির যেকোনো তিনটি সমরেখ নয়। AB, BC, CD ও DA রেখাংশ চারটি সংযোগে ABCD চতুর্ভুজ গঠিত হয়েছে। AB, BC, CD ও DA চতুর্ভুজটির চারটি বাহু। A, B, C ও D চারটি কৌণিক বিন্দু বা শীর্ষবিন্দু  ∠ABC, ∠BCD, ∠CDA ও ∠DAB চতুর্ভুজের চারটি কোণ। A ও B শীর্ষবিন্দু যথাক্রমে C ও D শীর্ষের বিপরীত শীর্ষবিন্দু। AB ও CD পরস্পর বিপরীত বাহু এবং AD ও BC পরস্পর বিপরীত বাহু। এক শীর্ষবিন্দুতে যে দুইটি বাহু মিলিত হয়, এরা সন্নিহিত বাহু। যেমন, AB ও BC বাহু দুইটি সন্নিহিত বাহু। AC ও BD রেখাংশদ্বয় ABCD চতুর্ভুজের দুইটি কর্ণ। চতুর্ভুজের বাহুগুলোর দৈর্ঘ্যের সমষ্টিকে এর পরিসীমা বলে। ABCD চতুর্ভুজের পরিসীমা (AB + BC + CD + DA) এর দৈর্ঘ্যের সমান। চতুর্ভুজকে অনেক সময় ‘☐’ প্রতীক দ্বারা নির্দেশ করা হয়।

common.content_added_and_updated_by
টপ রেটেড অ্যাপ

স্যাট অ্যাকাডেমী অ্যাপ

আমাদের অল-ইন-ওয়ান মোবাইল অ্যাপের মাধ্যমে সীমাহীন শেখার সুযোগ উপভোগ করুন।

ভিডিও
লাইভ ক্লাস
এক্সাম
ডাউনলোড করুন
Promotion
Request history8.2.28PHP Version82.71msRequest Duration7MBMemory UsageGET academy/{slug}Route
    • Booting (26.23ms)time
    • Application (56.48ms)time
    • 1 x Application (68.29%)
      56.48ms
      1 x Booting (31.71%)
      26.23ms
      49 templates were rendered
      • academy.subject.read_chapterread_chapter.blade.php#?blade
      • academy.include.sidebarListsidebarList.blade.php#?blade
      • academy.include.left_sidebar_menuleft_sidebar_menu.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • common.modal.self_test_modalself_test_modal.blade.php#?blade
      • common.modal.bookmark_modalbookmark_modal.blade.php#?blade
      • common.modal.error_report_modalerror_report_modal.blade.php#?blade
      • common.modal.video_modalvideo_modal.blade.php#?blade
      • common.script.page_type_scriptpage_type_script.blade.php#?blade
      • job.job_include.job_scriptjob_script.blade.php#?blade
      • common.script.activity_scriptactivity_script.blade.php#?blade
      • common.script.test_scripttest_script.blade.php#?blade
      • common.script.custom_dropdowncustom_dropdown.blade.php#?blade
      • common.script.follow_unfollow_scriptfollow_unfollow_script.blade.php#?blade
      • common.script.short_statistics_scriptshort_statistics_script.blade.php#?blade
      • common.script.navigator_sharenavigator_share.blade.php#?blade
      • layouts.satt-appsatt-app.blade.php#?blade
      • includes.header_link2header_link2.blade.php#?blade
      • laravelpwa::metameta.blade.php#?blade
      • layouts.headerheader.blade.php#?blade
      • layouts.toolbartoolbar.blade.php#?blade
      • frontend.downloadourappdownloadourapp.blade.php#?blade
      • frontend.referralreferral.blade.php#?blade
      • auth.user_type_modaluser_type_modal.blade.php#?blade
      • layouts.footerfooter.blade.php#?blade
      • common.login_modallogin_modal.blade.php#?blade
      • components.authentication-card-logoauthentication-card-logo.blade.php#?blade
      • common.includes.promotion_modalpromotion_modal.blade.php#?blade
      • common.includes.notification_item_modalnotification_item_modal.blade.php#?blade
      • common.includes.notification_item_list_modalnotification_item_list_modal.blade.php#?blade
      • common.includes.promotion_offcanvaspromotion_offcanvas.blade.php#?blade
      • includes.footer_link2footer_link2.blade.php#?blade
      • includes.restrictrestrict.blade.php#?blade
      • livewire-alert::components.scriptsscripts.blade.php#?blade
      • livewire-alert::components.flashflash.blade.php#?blade
      • admin.include.toastrtoastr.blade.php#?blade
      • common.search.search_scriptsearch_script.blade.php#?blade
      • common.script.promotion_scriptpromotion_script.blade.php#?blade
      • common.script.promotion_functionspromotion_functions.blade.php#?blade
      uri
      GET academy/{slug}
      middleware
      web, throttle:global
      controller
      App\Http\Controllers\Academy\SubjectController@chapter
      namespace
      prefix
      where
      as
      academy.subject.chapter
      file
      app/Http/Controllers/Academy/SubjectController.php:102-110
      21 statements were executed (4 duplicates)Show only duplicates34.61ms
      • SubjectRepository.php#94satt_satt_mobile_app160μsselect `id`, `main_category_id`, `parent_id`, `show_content` from `subjects` where `slug` = 'চতুর্ভুজ-quadrilateral-34347' and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: চতুর্ভুজ-quadrilateral-34347
        Backtrace
        • app/Repositories/SubjectRepository.php:94
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:91
        • app/Services/SubjectService.php:32
      • SubjectService.php#43satt_satt_mobile_app580μsupdate `subjects` set `view_count` = `view_count` + 1, `subjects`.`updated_at` = '2025-04-09 09:30:48' where `id` = 15347
        Bindings
        • 0: 2025-04-09 09:30:48
        • 1: 15347
        Backtrace
        • app/Services/SubjectService.php:43
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
      • QueryBuilder.php#38satt_satt_mobile_app130μsselect `_lft`, `_rgt` from `subjects` where `id` = 15347 limit 1
        Bindings
        • 0: 15347
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:60
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:235
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:227
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
      • QueryBuilder.php#305satt_satt_mobile_app190μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `show_content`, `num_of_mcq`, `num_of_written`, `des_added_by`, `des_updated_by`, `author_name`, `link_subject_id`, `sub_category_id`, `main_category_id`, `slug`, `meta_og_title`, `meta_keyword`, `meta_description`, `vote`, `view_count`, `icon`, `page_type`, `chapter_name` from `subjects` where (`subjects`.`_lft` between 39751 and 39752) and `subjects`.`deleted_at` is null
        Bindings
        • 0: 39751
        • 1: 39752
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305satt_satt_mobile_app170μsselect `id`, `description`, `short_description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (15347) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305satt_satt_mobile_app130μsselect `id`, `name`, `avatar` from `users` where `users`.`id` in (38332) and `users`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305satt_satt_mobile_app110μsselect `id`, `name`, `avatar` from `users` where `users`.`id` in (38332) and `users`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305satt_satt_mobile_app100μsselect `id`, `name`, `slug` from `sub_categories` where `sub_categories`.`id` in (4870) and `sub_categories`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305satt_satt_mobile_app130μsselect `id`, `user_id`, `completeable_type`, `completeable_id`, `complete_progress`, `is_complete` from `completes` where `completes`.`completeable_id` in (15347) and `completes`.`completeable_type` = 'App\\Models\\Subject'
        Bindings
        • 0: App\Models\Subject
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305satt_satt_mobile_app360μsselect * from (select `questions`.`id`, `questions`.`subject_id`, `questions`.`category_id`, `questions`.`sub_category_id`, `questions`.`board_exam_id`, `questions`.`passage_id`, `questions`.`question_type`, `questions`.`question`, `questions`.`is_duplicate`, `questions`.`status`, `questions`.`image`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, row_number() over (partition by `subjectables`.`subject_id` order by `questions`.`created_at` desc) as `laravel_row` from `questions` inner join `subjectables` on `questions`.`id` = `subjectables`.`subjectable_id` where `subjectables`.`subject_id` in (15347) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `questions`.`status` = 'active' and `questions`.`deleted_at` is null) as `laravel_table` where `laravel_row` <= 5 order by `laravel_row`
        Bindings
        • 0: App\Models\Question
        • 1: active
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • SubjectRepository.php#122satt_satt_mobile_app180μsselect * from `subjects` where `subjects`.`id` = 15347 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 15347
        Backtrace
        • app/Repositories/SubjectRepository.php:122
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:121
        • app/Services/SubjectService.php:60
      • SubjectRepository.php#125satt_satt_mobile_app30.81msselect `id`, `name`, `slug`, `parent_id`, `_lft`, `_rgt` from `subjects` where (39752 between `subjects`.`_lft` and `subjects`.`_rgt` and `subjects`.`id` <> 15347) and `subjects`.`deleted_at` is null order by `_lft` asc
        Bindings
        • 0: 39752
        • 1: 15347
        Backtrace
        • app/Repositories/SubjectRepository.php:125
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:121
        • app/Services/SubjectService.php:60
      • SubjectRepository.php#137satt_satt_mobile_app200μsselect * from `subjects` where `subjects`.`id` = 15347 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 15347
        Backtrace
        • app/Repositories/SubjectRepository.php:137
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:136
        • app/Services/SubjectService.php:61
      • SubjectRepository.php#140satt_satt_mobile_app140μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `slug`, `meta_og_title`, `meta_keyword`, `meta_description` from `subjects` where `subjects`.`id` = 7879 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 7879
        Backtrace
        • app/Repositories/SubjectRepository.php:140
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:136
        • app/Services/SubjectService.php:61
      • SubjectRepository.php#140satt_satt_mobile_app110μsselect `id`, `description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (7879) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • app/Repositories/SubjectRepository.php:140
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:136
        • app/Services/SubjectService.php:61
      • QueryBuilder.php#38satt_satt_mobile_app120μsselect `_lft`, `_rgt` from `subjects` where `id` = 7527 limit 1
        Bindings
        • 0: 7527
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:60
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:235
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:227
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
      • QueryBuilder.php#305satt_satt_mobile_app290μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `name`, `slug`, `icon`, `banner` from `subjects` where (`subjects`.`_lft` between 39615 and 39812) and `subjects`.`deleted_at` is null
        Bindings
        • 0: 39615
        • 1: 39812
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:293
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • SubjectRepository.php#325satt_satt_mobile_app150μsselect * from `mediables` where `mediable_type` = 'App\\Models\\Subject' and `mediable_id` in (15347)
        Bindings
        • 0: App\Models\Subject
        • 1: 15347
        Backtrace
        • app/Repositories/SubjectRepository.php:325
        • app/Services/SubjectService.php:76
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
      • SubjectRepository.php#340satt_satt_mobile_app130μsselect `videos`.`video_src_url`, `mediables`.`mediable_id` as `chapter_id` from `videos` inner join `mediables` on `mediables`.`mediable_id` = `videos`.`id` where `videos`.`id` = 0 and `videos`.`video_src` = 'youtube' and `videos`.`deleted_at` is null
        Bindings
        • 0: 0
        • 1: youtube
        Backtrace
        • app/Repositories/SubjectRepository.php:340
        • app/Services/SubjectService.php:77
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
      • SubjectService.php#82satt_satt_mobile_app210μsselect `id`, `name`, `main_category_id`, `slug` from `subjects` where `id` <> 15347 and `parent_id` = 7879 and `main_category_id` = 2 and `subjects`.`deleted_at` is null limit 5
        Bindings
        • 0: 15347
        • 1: 7879
        • 2: 2
        Backtrace
        • app/Services/SubjectService.php:82
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
      • restrict.blade.php#30satt_satt_mobile_app210μsselect * from `package_plans` where `status` = 'active' and `package_plans`.`deleted_at` is null
        Bindings
        • 0: active
        Backtrace
        • view::includes.restrict:30
        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • vendor/livewire/livewire/src/Mechanisms/ExtendBlade/ExtendedCompilerEngine.php:22
        • vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75
      App\Models\Subject
      106Subject.php#?
      App\Models\PackagePlan
      3PackagePlan.php#?
      App\Models\SubjectDescription
      2SubjectDescription.php#?
      App\Models\User
      2User.php#?
      App\Models\SubCategory
      1SubCategory.php#?
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