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It explains how to compute triangle counts using addition and multiplication of divided parts, then provides rules for square counting based on whether rows equal columns. Rectangle counting is shown for cases where row differs from column and where row equals column, using product and sum-based decompositions. The document concludes with 8 labeled practice questions (Q1–Q8) asking for numbers of triangles in given figures, including answer options and correct answers.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/tricks-for-counting-triangles-squares-and-rectangles-practice-questions/449987/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/tricks-for-counting-triangles-squares-and-rectangles-practice-questions/449987.png","ImageObject",300,407,{"name":92,"@type":93},"Elsa","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What trick is used to count triangles when parts are divided in different ways?","Question",{"text":112,"@type":113},"The notes use addition of divided parts and then multiply the summed result by the number of corresponding divisions, shown in stepwise products like (1+2) x 2, (1+2+3) x 3.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you count squares depending on whether the row equals the column?",{"text":117,"@type":113},"When row equals column, the document uses a sum of squares such as 1²+2²+3²+4². When row differs from column, it uses a decomposition like (4 x 3) + (3 x 2) + (2 x 1).",{"name":119,"@type":110,"acceptedAnswer":120},"What method is shown for counting rectangles for the cases Row ≠ column and Row = Column?",{"text":121,"@type":113},"For Row ≠ column, it uses row x column and also an expanded product of sums like (1+2+3) x (1+2+3+4). For Row = Column, it uses row x column and an expanded product like (1+2+3+4) x (1+2+3+4) resulting in 100 for 10 x 10.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},449987,1790813829,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},137455077381,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Before moving on to the practice questions let us have a look at some of the tricks important for the counting of triangles, rectangles and squares, that would be very helpful in solving the questions andwill make them easy.  \nTRICKS FOR TRIANGLES  \nADDITION OF DIVIDED PARTS  \n= 1+2  \n= 3  \n= 1+2+3  \n= 6  \n= 1+2+3+4  \n= 1+2+3+4+5  \n= 15  \nWHEN PARTS ARE DIVIDED IN PARTS  \n= (1+2) x 2  \n= 3x2  \n= 6  \n= (1+2+3) x 2  \n= 6 x 2  \n= 12  \n= (1+2+3) x 3  \n= 6 x3  \n= 18  \n= (1+2+3+4+5) x 5  \n= 15 x5  \n= 75  \nTRICKS FOR COUNTING SQUARES • When row is equal to column.  \n• When row is not equal to column. SQUARE  \nWhen row = column  \nR = 4  \nC = 4  \n1²+ 2² + 3² + 4² = 30  \nWhen row ≠ column  \nR = 3  \nC = 4  \n= (4 x3) + (3 x 2) + (2 x1)  \n= 12+6+2  \n= 20  \nTRICKS FOR COUNTING RECTANGLES  \n• When Row = Column  \n• When Row ≠ Column  \nWhen Row ≠ column  \nR = 3  \nC = 4  \n= row x column  \n= (1+2+3) x (1+2+3+4)  \n= 6 x 10  \n= 60  \nWhen Row = Column  \nR = 4  \nC = 4  \n= row x column  \n= (1+2+3+4) x (1+2+3+4)=> 10 x 10 = 100  \nHOW MANY TRIANGLES  \n= (4 x 2) + (4 x 2)= 8 + 8  \n= 16+ (2)  \n= 18  \n= (8 x 2) + (1+2)= 16+ 3  \n= 19 + (2)  \n= 21  \n= (4x2) + (4x2) + (4x2)= 8+8+8  \n= 24+4  \n= 28  \n50 Important Counting Figures Practice Questions Q1) In the following question number of triangles are  \n(a) 21  \n(b) 23  \n(c) 25  \n(d) 27  \nCorrect Answer: “d”  \nQ2) Find the number of triangles in the given figure  \n(a) 12  \n(b) 18  \n(c) 22  \n(d) 26  \nCorrect Answer: “b”  \nQ3) How many triangles are there in the given figure?  \n(a) 20  \n(b) 23  \n(c) 24  \n(d) 26  \nCorrect Answer: “a”  \nQ4) How many triangles are there in the given figure?  \n(a) 18  \n(b) 19  \n(c) 20  \n(d) 21  \nCorrect Answer: “c”  \nQ5) How many triangles are there in the given figure?  \n(a) 28  \n(b) 36  \n(c) 40  \n(d) 48  \nCorrect Answer: “b”  \nQ6) How many triangles are there in the given figure?  \n(a) 29  \n(b) 38  \n(c) 40  \n(d) 35  \nCorrect Answer: “c”  \nQ7) How many triangles are there in the given figure?  \n(a) 32  \n(b) 34  \n(c) 37  \n(d) 40  \nCorrect Answer: “c”  \nQ8) Find the number of triangles in the given figure?  \n(a) 27  \n(b) 25  \n(c) 23  \n(d) 21  \nCorrect Answer: “a”","cbCaieQvnRMAjG6i","https://ap.wps.com/l/cbCaieQvnRMAjG6i","pdf",1768473,54,"English","# Tricks for Triangles\n## Addition of Divided Parts\n# Tricks for Counting Squares\n## When row equals column\n## When row not equal column\n# Tricks for Counting Rectangles\n## When Row ≠ column\n## When Row = Column\n# How many triangles (example computations)\n# 50 Important Counting Figures Practice Questions (Q1–Q8)","[{\"question\":\"What trick is used to count triangles when parts are divided in different ways?\",\"answer\":\"The notes use addition of divided parts and then multiply the summed result by the number of corresponding divisions, shown in stepwise products like (1+2) x 2, (1+2+3) x 3.\"},{\"question\":\"How do you count squares depending on whether the row equals the column?\",\"answer\":\"When row equals column, the document uses a sum of squares such as 1²+2²+3²+4². When row differs from column, it uses a decomposition like (4 x 3) + (3 x 2) + (2 x 1).\"},{\"question\":\"What method is shown for counting rectangles for the cases Row ≠ column and Row = Column?\",\"answer\":\"For Row ≠ column, it uses row x column and also an expanded product of sums like (1+2+3) x (1+2+3+4). For Row = Column, it uses row x column and an expanded product like (1+2+3+4) x (1+2+3+4) resulting in 100 for 10 x 10.\"}]","Tricks for Counting Triangles, Squares and Rectangles - Practice Questions | PDF",1790731709,136]