1) What’s the area of an equilateral triangle with side 5? (Please...

Question
1) What’s the area of an equilateral triangle with side 5? (Please explain how you got your answer).

2) What’s the area of each of the triangles with the following sides:
a) 5, 12, 13
b) 4, 6, 8
c) 4, 6, 10
d) 4, 6, 11 (Explain the answers for parts c) and d)).

3) If a polygon has seven sides, what’s the sum of the all the angles?
4) If a regular polygon has eight sides, what is the measure of each angle?
5) If a polygon has six sides, how many diagonals does it have?
6) If I tell you that a polygon has 55 diagonals, can you tell me how many sides it has?
7) What would you call a polygon with twenty sides? Why?
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4) The sum of interior angles for the polygon with 8 sides is 180*(8-2)= 180*6=1080 degrees. Since we are told the polygon is regular => all interior angles have the same size equal with 1080/8=135 degrees.
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      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (404μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • creating: site.layouts.app (414μs)
      • composing: site.layouts.app (18μs)
      • creating: components.canonical (557μs)
      • composing: components.canonical (107μs)
      • creating: components.open-graph (214μs)
      • composing: components.open-graph (171μs)
      • creating: site.headers.header (344μs)
      • composing: site.headers.header (81μs)
      • Illuminate\Cache\Events\CacheHit (2.81ms)
      • creating: components.footer (314μs)
      • composing: components.footer (106μs)
      • Illuminate\Cache\Events\CacheHit (1.06ms)
      • Illuminate\Cache\Events\CacheMissed (387μs)
      • Illuminate\Database\Events\StatementPrepared (718μs)
      • Illuminate\Database\Events\QueryExecuted (1.62ms)
      • eloquent.retrieved: App\Models\SubjectCat (60μs)
      • Illuminate\Cache\Events\KeyWritten (1.57ms)
      • Illuminate\Cache\Events\CacheHit (305μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (515μs)
      • Illuminate\Cache\Events\CacheHit (488μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (314μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • creating: components.forms.contact-us (219μs)
      • composing: components.forms.contact-us (151μs)
      • creating: components.forms.get-started (146μs)
      • composing: components.forms.get-started (72μs)
      • creating: components.forms.free-tool-download (172μs)
      • composing: components.forms.free-tool-download (73μs)
      • creating: components.forms.claim-free-worksheet (112μs)
      • composing: components.forms.claim-free-worksheet (67μs)
      • creating: components.forms.tutor-subscription-waitlist (99μs)
      • composing: components.forms.tutor-subscription-waitlist (65μs)
      • creating: components.forms.tutor-subscription-join (100μs)
      • composing: components.forms.tutor-subscription-join (66μs)
      • creating: components.forms.tutor-support (100μs)
      • composing: components.forms.tutor-support (63μs)
      • 311 x Illuminate\Cache\Events\CacheHit (17.93%)
        93.25ms
        20 x Illuminate\Database\Events\StatementPrepared (6.2%)
        32.23ms
        20 x Illuminate\Database\Events\QueryExecuted (5.39%)
        28.03ms
        11 x Illuminate\Cache\Events\KeyWritten (2.14%)
        11.14ms
        11 x Illuminate\Cache\Events\CacheMissed (1.85%)
        9.61ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.58%)
        3.02ms
        1 x Illuminate\Routing\Events\Routing (0.21%)
        1.12ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.21%)
        1.08ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.16%)
        814μs
        1 x creating: components.canonical (0.11%)
        557μs
        1 x eloquent.booting: App\Models\SubjectCat (0.1%)
        534μs
        1 x creating: homework.show (0.09%)
        469μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.08%)
        440μs
        1 x creating: site.layouts.app (0.08%)
        414μs
        1 x creating: components.breadcrumbs (0.07%)
        359μs
        1 x creating: site.headers.header (0.07%)
        344μs
        1 x creating: components.footer (0.06%)
        314μs
        5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.06%)
        290μs
        1 x Illuminate\Routing\Events\RouteMatched (0.05%)
        254μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        247μs
        1 x creating: components.forms.contact-us (0.04%)
        219μs
        1 x creating: components.open-graph (0.04%)
        214μs
        1 x composing: homework.show (0.04%)
        189μs
        1 x composing: components.breadcrumbs (0.03%)
        173μs
        1 x creating: components.forms.free-tool-download (0.03%)
        172μs
        1 x composing: components.open-graph (0.03%)
        171μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        170μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        162μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        159μs
        1 x composing: components.forms.contact-us (0.03%)
        151μs
        1 x creating: components.forms.get-started (0.03%)
        146μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        112μs
        1 x composing: components.canonical (0.02%)
        107μs
        1 x composing: components.footer (0.02%)
        106μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        102μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        100μs
        1 x creating: components.forms.tutor-support (0.02%)
        100μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        99μs
        1 x composing: site.headers.header (0.02%)
        81μs
        1 x composing: components.forms.free-tool-download (0.01%)
        73μs
        1 x composing: components.forms.get-started (0.01%)
        72μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        67μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        66μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        65μs
        1 x composing: components.forms.tutor-support (0.01%)
        63μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        62μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        59μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        41μs
        1 x composing: site.layouts.app (0%)
        18μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated37.81ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '25926' limit 1
        10.79mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 25926
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (3)
        1mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (25926)
        4.3mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 25926 and `subject` = 3 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        3.53mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 25926
        • 1: 3
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (3)
        920μstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 25926 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.29mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 25926
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 25926 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.2mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 25926
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 25926 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.05mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.08mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.17mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.17mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.16mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.12mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.38mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.11mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.22mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.31mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      5HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
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          utm_source
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          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Geo...
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          PHPDEBUGBAR_STACK_DATA
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          status_code
          200
          
          status_text
          OK
          format
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          content_type
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          request_request
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          request_headers
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          request_cookies
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