{"id":5838,"date":"2021-03-06T10:21:16","date_gmt":"2021-03-06T04:51:16","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=5838"},"modified":"2021-09-15T11:39:28","modified_gmt":"2021-09-15T06:09:28","slug":"ap-board-9th-class-maths-solutions-chapter-11-intext-questions","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-9th-class-maths-solutions-chapter-11-intext-questions\/","title":{"rendered":"AP Board 9th Class Maths Solutions Chapter 11 Areas InText Questions"},"content":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions<\/a> Chapter 11 Areas InText Questions\u00a0and Answers.<\/p>\n

AP State Syllabus 9th Class Maths Solutions 11th Lesson Areas InText Questions<\/h2>\n

\"AP<\/p>\n

Activity<\/strong><\/p>\n

Question
\n\"AP<\/p>\n

Observe Figure I and II. Find the area of both. Are the areas equal?
\nTrace these figures on a sheet of paper, cut them. Cover fig. 1 with fig. II. Do they cover each other completely? Are they congruent?
\nObserve fig. Ill and IV. Find the areas of both. What do you notice?
\nAre they congruent?
\nNow, trace these figures on sheet of paper. Cut them let us cover fig. Ill by fig. IV by coinciding their bases (length of same side).
\nAs shown in figure V are they covered completely?
\nWe conclude that Figures I and II are congruent and equal in area. But figures III and IV are equal in area but they are not congruent
\n\"AP<\/p>\n

Think, Discuss and Write<\/strong><\/p>\n

Question 1.
\nIf 1 cm represents 5 in, what would be an area of 6 cm2<\/sup> represents ?
\n[Page No. 247]
\nSolution:
\n1 cm2<\/sup> = 5 m
\n1 cm2<\/sup> = 1 cm \u00d7 1 cm = 5m \u00d7 5m = 25m2<\/sup>
\n\u2234 6 cm2<\/sup> = 6 \u00d7 25 m2<\/sup> = 150 m2<\/sup><\/p>\n

Question 2.
\nRajni says 1 sq. m = 1002<\/sup> sq. cm. Do you agree ? Explain.
\nSolution:
\nNo
\n1 sq. m = 100 cm2<\/sup><\/p>\n

\"AP<\/p>\n

Think, Discuss and Write<\/strong><\/p>\n

Question
\nWhich of the following figures lie on the same base and between the same parallels? In such cases, write the common base and two parallels. [Page No. 249]
\n\"AP
\nSolution:
\na) In figure (a) \u0394PCD and \u25a1 ABCD lie on same base CD and between the same parallels AB\/\/CD.
\nb) No,
\nc) \u0394TRQ and \u25a1 PQRS lie on the same base QR and between the same par-allels PS\/\/QR.
\nd) \u0394APD and \u25a1 ABCD lie on the same base AD and between the same par-allels AD\/\/BC.
\ne) No.<\/p>\n

Activity<\/strong><\/p>\n

Question
\nTake a graph sheet and draw two par-allelograms ABCD and PQCD on it as show in the Figure, [Page No. 250]
\n\"AP
\nThe parallelograms are on the same base DC and between the same parallels PB and DC. Clearly the part DCQA is common between the two parallelo-grams. So if we can show that \u0394DAP and \u0394CBQ have the same area then we can say ar(PQCD) = ar(ABCD)<\/p>\n

\"AP<\/p>\n

Activity<\/strong><\/p>\n

Draw pairs of triangles one the same base or ( equal bases) and between the same parallels on the graph sheet as shown in the Figure.
\nLet AABC and ADBC be the two triangles lying on the same base BC and between parallels BC and FE.
\nDraw CE II AB and BF II CD. Parallelograms AECB and FDCB are on the same base BC and are between the same parallels BC and EF.
\n\"AP
\nThus ar (AECB) = ar (FDCB).
\nWe can see ar (\u0394ABC) = \\(\\frac { 1 }{ 2 }\\) ar (parallelogram AECB) …………….(i)
\nand ar (\u0394DBC) = \\(\\frac { 1 }{ 2 }\\) ar (parallelogram FDCB) ……………..(ii)
\nFrom (i) and (ii), we get ar (\u0394ABC) = ar (\u0394DBC)
\nYou can also find the areas of \u0394ABC and \u0394DBC by the method of counting the squares in graph sheet as we have done in the earlier activity and check the areas are whether same.[Page No. 254]
\n\"AP<\/p>\n

\"AP<\/p>\n

Think, Discus and Write<\/strong><\/p>\n

Draw two triangles ABC and DBC on the same base and between the same parallels as shown in the figure with P as the point of intersection of AC and BD. Draw CE\/\/BA and BF\/\/CD such that E and F lie on line AD.
\nCan you show ar(\u0394PAB) = ar(\u0394PDQ) ?[Page No. 254]
\n\"AP
\n[Hint: These triangles are not congruent but have equal areas.
\nSolution:
\n\u25a1 ABCE = 2 \u00d7 \u0394ABC
\n[\u2235 \u0394ABC; \u25a1ABCE lie on the same base BC and between the same parallels BC \/\/ AE]
\n\u0394ABC = \\(\\frac { 1 }{ 2 }\\) \u00d7 \u25a1 ABCE ……………(1)
\nAlso \u25a1 BCDF = 2 \u00d7 \u0394BCD…………..
\n[\u2235\u0394BCD and \u25a1 BCDE lie on the same base BC and between , the same parallels BC\/\/DE]
\n\u0394BCD = \\(\\frac { 1 }{ 2 }\\) \u00d7 \u25a1 BCDF ……………… (2)
\nBut \u25a1ABCE = \u25a1BCDF
\n[ \u2235 \u25a1ABCE and \u25a1BCDF lie on the same base BC and between the same parallels BC\/\/FE]
\nFrom (1) & (2); \u0394ABC = \u0394BCD
\n\u0394PAB + \u0394PBC = \u0394PBC + \u0394PDC
\n\u21d2 \u0394PAB = \u0394PDC
\nHence proved.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions Chapter 11 Areas InText Questions\u00a0and Answers. AP State Syllabus 9th Class Maths Solutions 11th Lesson Areas InText Questions Activity Question Observe Figure I and II. Find the area of both. Are the areas equal? Trace these figures on a sheet of paper, cut them. Cover fig. 1 …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/5838"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=5838"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/5838\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=5838"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=5838"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=5838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}