{"id":12296,"date":"2018-03-09T15:00:06","date_gmt":"2018-03-09T09:30:06","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=12296"},"modified":"2018-03-09T15:00:06","modified_gmt":"2018-03-09T09:30:06","slug":"cat-questions-on-polygons-with-solutions","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/cat-questions-on-polygons-with-solutions\/","title":{"rendered":"CAT Questions on Polygons With Solutions"},"content":{"rendered":"

CAT Questions on Polygons With Solutions:<\/span><\/strong><\/p>\n

Geometry Polygons questions and answers for CAT. Polygons problems with solutions for CAT exam. Download excellent CAT preparation app to directly solve and practice questions.<\/p>\n

Download CAT App to Access this on your mobile<\/a><\/p>\n

25 Mocks + 30 Sectionals for Rs. 1249<\/a><\/p>\n

Download CAT Quant Questions PDF<\/a><\/p>\n

Take Free Mock Test for CAT 2018<\/a><\/p>\n

Question 1:\u00a0If the sum of interior angles of a polygon is 900 degrees, what is the number of diagonals it has?<\/p>\n

a) 9
\nb) 14
\nc) 20
\nd) None of these<\/p>\n

Question 2:\u00a0In a regular pentagon PQRST, what is the ratio of the area of triangle PRS to the area of the pentagon PQRST?<\/p>\n

a) 1 \/ (sin 72 + 4)
\nb) 1 \/ (cos 72 + 4)
\nc) 1 \/ (4 cos 72 + 1)
\nd) 1 \/ (4 sin 72 + 1)<\/p>\n

Question 3:\u00a0A regular polygon P has 135 diagonals. Find the exterior angle of the polygon P.<\/p>\n

a) $$18^{\\circ}$$
\nb) $$20^{\\circ}$$
\nc) $$25^{\\circ}$$
\nd) $$30^{\\circ}$$<\/p>\n

Download CAT 2018 Syllabus PDF<\/a><\/p>\n

Question 4:\u00a0A cylindrical pencil consists of a layer of wood surrounding a solid cylinder of graphite. The radius of the pencil is 6 mm, the radius of the graphite cylinder is 2 mm and the length of the pencil is 10 cm. Find the cost of the material used in a pencil, if the cost of wood is Rs. 0.70\/cm3 and that of graphite is Rs. 2.80\/cm3.<\/p>\n

a) Rs. 7.85
\nb) Rs. 8.76
\nc) Rs. 9.36
\nd) Rs. 10.56<\/p>\n

Question 5:\u00a0If the shortest diagonal in a regular hexagon is 10 cm, what is the length of the longest diagonal (in cm)? Round your answer to the nearest integer. Given $$\\sqrt3 = 1.732$$.<\/p>\n

a) 12
\nb) 13
\nc) 14
\nd) 15<\/p>\n

Solutions for\u00a0CAT Questions on Polygons With Solutions:<\/strong><\/span><\/p>\n

Solutions:<\/strong><\/p>\n

1) Answer (B)<\/strong><\/p>\n

The sum of interior angles for an \u2018n\u2019 sided polygon is (2n-4) \\times 90 degrees.
\nIf this value is 900, then the polygon is a heptagon.
\nThe number of diagonals for an \u2018n\u2019 sided polygon = $$ \\frac{n(n-3)}{2}$$
\n= 14 for a heptagon.<\/p>\n

Factors of a number – Formulas for CAT<\/a><\/p>\n

Formulas on Number system and factorials\u00a0<\/a><\/p>\n

2) Answer (C)<\/strong><\/p>\n

Each angle of a regular pentagon is 108 degrees. In triangle PTS, angle T = 108 degrees, and PT = TS. So, angle TPS = angle TSP = 36 degrees.
\nSimilarly, angle QPR = 36 degrees. So, angle SPR = 108 – (36 + 36) = 36 degrees
\nAlso, PS = PR
\nArea of triangle PSR = \u00bd * PS * PR * sin 36
\nArea of the pentagon = Sum of areas of the three triangles = Area of triangle PTS + Area of triangle PSR + Area of triangle PQR
\n= \u00bd * PT * PS * sin (angle TPS) + \u00bd * PS * PR * sin 36 + \u00bd * PQ * PR * sin (angle QPR)
\n= \u00bd * PT * PS * sin 36 + \u00bd * PS * PR * sin 36 + \u00bd * PQ * PR * sin 36
\nRequired ratio = \u00bd * PS * PR * sin 36 \/ (\u00bd * PT * PS * sin 36 + \u00bd * PS * PR * sin 36 + \u00bd * PQ * PR * sin 36)
\n= PR \/ (PT + PR + PQ)
\nPT = PQ = SR
\nSR = 2 * PR cos (angle PSR) = 2 * PR * cos 72
\nRatio = PR \/ (2 * PR cos 72 + PR + 2 * PR cos 72) = 1 \/ (4 cos 72 + 1)<\/p>\n

3) Answer (B)<\/strong><\/p>\n

Number of diagonals in a regular polygon = $$^nC_2 – n$$
\n=> $$^nC_2 – n$$ = 135
\n=> n = 18
\nExterior angle = $$\\frac{360}{n}$$ = $$\\frac{360}{18}$$ = $$20^{\\circ}$$<\/p>\n

4) Answer (D)<\/strong><\/p>\n

Volume of the whole pencil = $$3.6\\pi$$ cm^3
\nVolume of graphite cylinder = $$0.4\\pi$$ cm^3
\nVolume of wood part = $$3.6\\pi-0.4\\pi=3.2\\pi$$ cm^3
\nCost of the pencil
\n= $$3.2\\times\\frac{22}{7}\\times0.7+0.4\\times\\frac{22}{7}\\times2.8$$
\n= Rs. 10.56<\/p>\n

5) Answer (A)<\/strong><\/p>\n

<\/p>\n

Measure of internal angle in a regular hexagon = 120 degrees
\nDiagonal AD bisects angle EDC. So, angle EDA = 60 degrees
\nIn triangle AED, angle AED = 90 degrees, angle ADE = 60 degrees
\nAE is the shortest diagonal of the hexagon and AD is the longest diagonal.
\nAE = 10 cm
\nSin 60 = AE\/AD => AD = AE\/sin 60 = $$10\/(\\sqrt3\/2)$$ = $$20\/\\sqrt3$$ cm = 20\/1.732 = 11.54 cm = 12 cm (approx.)<\/p>\n

Polygons CAT questions with solutions, practice problems with detailed explanations.<\/p>\n

Take a free CAT online mock test<\/a><\/p>\n

CAT Online Most Trusted Courses<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

CAT Questions on Polygons With Solutions: Geometry Polygons questions and answers for CAT. Polygons problems with solutions for CAT exam. Download excellent CAT preparation app to directly solve and practice questions. Download CAT Quant Questions PDF Take Free Mock Test for CAT 2018 Question 1:\u00a0If the sum of interior angles of a polygon is 900 […]<\/p>\n","protected":false},"author":21,"featured_media":12299,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,125],"tags":[422],"class_list":{"0":"post-12296","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-cat","8":"category-downloads","9":"category-featured","10":"tag-cat-2018"},"better_featured_image":{"id":12299,"alt_text":"CAT Questions on Polygons With Solutions","caption":"CAT Questions on Polygons With Solutions","description":"CAT Questions on Polygons With Solutions","media_type":"image","media_details":{"width":"960","height":"504","file":"2018\/03\/fig-09-03-2018_06-04-03.jpg","sizes":{"thumbnail":{"file":"fig-09-03-2018_06-04-03-150x150.jpg","width":"150","height":"150","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-150x150.jpg"},"medium":{"file":"fig-09-03-2018_06-04-03-300x158.jpg","width":"300","height":"158","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-300x158.jpg"},"medium_large":{"file":"fig-09-03-2018_06-04-03-768x403.jpg","width":"768","height":"403","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-768x403.jpg"},"tiny-lazy":{"file":"fig-09-03-2018_06-04-03-30x16.jpg","width":"30","height":"16","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-30x16.jpg"},"td_80x60":{"file":"fig-09-03-2018_06-04-03-80x60.jpg","width":"80","height":"60","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-80x60.jpg"},"td_100x70":{"file":"fig-09-03-2018_06-04-03-100x70.jpg","width":"100","height":"70","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-100x70.jpg"},"td_218x150":{"file":"fig-09-03-2018_06-04-03-218x150.jpg","width":"218","height":"150","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-218x150.jpg"},"td_265x198":{"file":"fig-09-03-2018_06-04-03-265x198.jpg","width":"265","height":"198","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-265x198.jpg"},"td_324x160":{"file":"fig-09-03-2018_06-04-03-324x160.jpg","width":"324","height":"160","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-324x160.jpg"},"td_324x235":{"file":"fig-09-03-2018_06-04-03-324x235.jpg","width":"324","height":"235","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-324x235.jpg"},"td_324x400":{"file":"fig-09-03-2018_06-04-03-324x400.jpg","width":"324","height":"400","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-324x400.jpg"},"td_356x220":{"file":"fig-09-03-2018_06-04-03-356x220.jpg","width":"356","height":"220","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-356x220.jpg"},"td_356x364":{"file":"fig-09-03-2018_06-04-03-356x364.jpg","width":"356","height":"364","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-356x364.jpg"},"td_533x261":{"file":"fig-09-03-2018_06-04-03-533x261.jpg","width":"533","height":"261","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-533x261.jpg"},"td_534x462":{"file":"fig-09-03-2018_06-04-03-534x462.jpg","width":"534","height":"462","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-534x462.jpg"},"td_696x0":{"file":"fig-09-03-2018_06-04-03-696x365.jpg","width":"696","height":"365","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-696x365.jpg"},"td_696x385":{"file":"fig-09-03-2018_06-04-03-696x385.jpg","width":"696","height":"385","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-696x385.jpg"},"td_741x486":{"file":"fig-09-03-2018_06-04-03-741x486.jpg","width":"741","height":"486","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-741x486.jpg"},"td_0x420":{"file":"fig-09-03-2018_06-04-03-800x420.jpg","width":"800","height":"420","mime-type":"image\/jpeg","source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03-800x420.jpg"}},"image_meta":{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}},"post":null,"source_url":"https:\/\/cracku.in\/blog\/wp-content\/uploads\/2018\/03\/fig-09-03-2018_06-04-03.jpg"},"yoast_head":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\t\n\t\n\n\n\n