Grade 7 / Parallelepiped 35 exercises (including 15 corrected)

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abcdefg ab ABCDEFGH F1F2F3 ChingQuizz : 1 exercise available for Quizz assessment : 1. Solid names E.11115 Give the name of each of the solids below : E.11116 For each of the solids below, decompose each into ˇ elementary ı solids. 2. Solid: vertices, edges, faces E.2676 The following figure shows the rect-angular parallelepiped ABCDEFGH : In this rectangular parallelepiped, 1 Name all the vertices. 2 Name all its edges. 3 Name all its faces. E.6459 Three solids are shown below : Complete the table below : F 1 F 2 F 3 Number of vertices Number of edges Number of faces https://chingmath.fr sacados/11115 abcdefg sacados/11116 ab chapExoCorrec/2676 sacados/2676 ABCDEFGH chapExoCorrec/6459 sacados/6459 F1F2F3
Fig.1Fig.4Fig.2Fig.3 ABCDEFGHIJKLMNOPQRSTUV abc ABCDEFGH ABCDEFGH E.10540 Consider the four solids below : Complete the table below : Fig. 1 Fig. 2 Fig. 3 Fig. 4 Number of vertices Number of edges Number of faces E.10541 Consider the two straight prisms ABCDEF and GHIJKLMNOPQRSTUV shown below : For each of these solids, give the number of vertices, edges, faces it has. E.11117 Consider the three solids below : Complete the table : Solid Nombre de faces Nombre d’arêtes Nombre de sommets a b c 3. Property of the right block E.6460 Opposite is a right block ABCDEFGH : 1 What is the nature of the quadrilateral BFGC ? 2 What can be said about the straight lines ( AD ) and ( AE ) ? 3 What can we say about the straight lines ( BC ) and ( EH ) ? 4 Are the straight lines ( HF ) and ( AG ) secant? E.11141 We consider the cube shown here in cavalier perspective. 1 Place the points : I mid-dle of the segment [ FB ] , J middle of [ BC ] , K mid-dle of [ CG ] , L middle of [ GF ] . 2 a Represent the face BCGF and the quadri-lateral IJKL in full size. b What is the nature of the quadrilateral IJKL ? https://chingmath.fr chapExoCorrec/10540 sacados/10540 Fig.1Fig.4Fig.2Fig.3 chapExoCorrec/10541 sacados/10541 ABCDEFGHIJKLMNOPQRSTUV sacados/11117 abc chapExoCorrec/6460 sacados/6460 ABCDEFGH sacados/11141 ABCDEFGH
ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ F1F2F3F4 P3P4P1P2 ABCDEFGHIJKLMNOP abcdef cdab E.11153 Consider the three polyhedra shown be-low in cavalier perspective : 1 Give the nature of each of these solids. 2 For each of these solids, name a face parallel to the col- ored face. E.11191 Consider the three polyhedra shown be-low in cavalier perspective : For each edge highlighted on the figure, name at least two edges perpendicular to it. 4. Equestrian perspectives E.6463 Consider the four cubes shown be-low : and four representations in cavalier perspective of cubes : Connect each of the cubes with its cavalier perspective repre-sentation. E.6462 The grid below will be used as a sup-port for the cavalier perspective representation of two cubes : 1 Represent the cube ABCDEFGH such that face ABFE is the front face. 2 Represent the cube IJKLMNOP such that face IJNM is the front face. E.11139 Which of the following are cavalier per-spective representations of parallelepipeds? E.11142 Below are given 4 unfinished representations of right pavers in cavalier perspective. Complete these four representations. https://chingmath.fr sacados/11153 ABCDEFGHIJKLMNOPQRSTUVWXYZ sacados/11191 ABCDEFGHIJKLMNOPQRSTUVWXYZ chapExoCorrec/6463 sacados/6463 F1F2F3F4 P3P4P1P2 chapExoCorrec/6462 sacados/6462 ABCDEFGHIJKLMNOP sacados/11139 abcdef chapExoCorrec/11142 sacados/11142 cdab
ABCDEFGHIJKLMN E.6461 Below is a cavalier perspective of a cube : Reproduce this cavalier perspective on the space left free on the right. E.2677 Four cavalier perspective represen-tations of rectangular parallelepipeds are incompletely shown below : Draw the missing continuous and dashed lines to complete their cavalier perspectives. 5. Cut out a pattern and build a solid E.6457 Below is given the pattern of a cube : 1 When the cube is completed, determine : a with which segment the segment [ EC ] will be superim- posed ; b with which segment the segment [ KL ] will be superim-posed ; c with which (s) point (s) will overlap the point H ; d with which (s) point (s) will overlap the point I . 2 Cut out, then construct this cube. https://chingmath.fr chapExoCorrec/6461 sacados/6461 chapExoCorrec/2677 sacados/2677 chapExoCorrec/6457 sacados/6457 ABCDEFGHIJKLMN
cab E.6458 Dice with 6 faces verify the following two rules : The faces of the numbers 1 , 2 and 3 must have one point in common ; The sum of two opposite faces must always be 7 . Below is given the pattern of a die with 6 faces où where the numbers 1 , 2 and 3 are shown : 1 Correctly place the numbers 4 , 5 and 6 on the pattern. 2 Cut out, then build the die. 6. Patterns E.11118 Justify that each of the representations below is not a pattern of a right-angled parallelepiped : https://chingmath.fr chapExoCorrec/6458 sacados/6458 sacados/11118 cab
dcbfae abcdef 4cmABCDE120o3cm E.11121 Below are given 6 patterns of solids : For each of these patterns, give the nature of the associated solid. E.11122 Which of the configurations below are patterns of rectangular parallelepipeds? 7. Create a pattern E.11147 Using the cube pattern shown opposite as a guide, construct a pattern for a straight block with the following dimensions : L =4 cm ; ‘ =3.5 cm ; h =2 cm E.11210 Using the cube pattern shown opposite as a guide, construct a pattern for a straight block with the following dimensions : L =3 cm ; ‘ =2 cm ; h =1.5 cm E.11211 Using the cube pattern shown opposite as a guide, construct a pattern for a straight block with the following dimensions : L =4 cm ; ‘ =3 cm ; h =2 cm E.11135 Consider the right prism with a pen-tagonal base shown below : 1 In actual size, create a pattern for this prism based on the following model : 2 Cut out and assemble the solid. 8. Thinking about bosses E.11143 Consider the two straight paving stone patterns given below : https://chingmath.fr sacados/11121 dcbfae sacados/11122 abcdef sacados/11147 chapExoCorrec/11210 sacados/11210 chapExoCorrec/11211 sacados/11211 chapExoCorrec/11135 sacados/11135 4cmABCDE120o3cm sacados/11143
3cm3;4cm3;2cmxyza2cm2;4cm2;2cmbxyz 2cm2;4cm2;2cm 12345 For each of them, give the length of the edges indicated in bold and marked ˇ x ı, ˇ y ı, ˇ z ı. E.11144 The representation below is not the pat-tern of a right block. Justify why. E.11146 To obtain a die with 6 faces, its faces must be numbered according to the following two rules : if we look at the 1 opposite and the 2 is on the right then the 3 must be the top face. if we sum the numbers of 2 opposite faces, we should get 7 . Correctly fill in the numbers on the faces to obtain a die with 6 faces : E.11208 Note: To obtain a 6 -sided die, you must number its sides according to the following two rules : If you look at the 1 side and the 2 side is on the right, then the 3 side must be the top side. if you add up the numbers on the 2 opposite sides, you must get 7 . Fill in the numbers on the sides correctly to obtain a 6 -sided die : E.11209 Note: To obtain a 6 -sided die, you must number its sides according to the following two rules : If you look at the 1 side and the 2 side is on the right, then the 3 side must be the top side. if you add up the numbers on the 2 opposite sides, you must get 7 . Complete the pattern below to obtain a " 6 "-sided die : 9. Seen from space E.11123 Consider the following assem-bly composed of cubes of iden-tical dimensions, each bearing the same pattern on its face. Among the 5 views shown be-low, find the front view (1) , the rear view (2) , the right view (3) , the left view (4) , and the top view (5) . https://chingmath.fr 3cm3;4cm3;2cmxyza2cm2;4cm2;2cmbxyz sacados/11144 2cm2;4cm2;2cm sacados/11146 sacados/11208 sacados/11209 sacados/11123 12345
abcde 12345 abcde 123456 face de droitefacededroite abcdef E.11119 Consider the following assem-bly composed of cubes of iden-tical dimensions, each bearing the same pattern on its face. Among the 5 views shown be-low, find the front view (1) , the rear view (2) , the right view (3) , the left view (4) , and the top view (5) . E.11136 Consider the following assembly of identically sized cubes with the same pattern on each face : Make a ˇflatı representation of each of the 6 ˇfaceı views of this solid. Hint: cube faces whose symbol cannot be known will be marked with a ˇ?ı sign. E.11120 Consider the solid constructed from a cube (composed of small cubes) where, on each of its faces, a row of small cubes has been removed : Each of these faces has been coated with fresh paint of a dif-ferent color. Then, the imprint of each of its faces was left on a piece of paper. Here are their representations : Associate each of these prints with one of the views of the cube (front, back, top, bottom, left, right) . https://chingmath.fr abcde sacados/11119 12345 abcde sacados/11136 123456 sacados/11120 face de droitefacededroite abcdef