(%i1) "Cornelsen, S. 97/Nr. 16"$

(%i2) "a) Eckpunktkoordinaten"$

(%i3) "D(0|0|0), C(0|8|0), B(8|8|0)"$

(%i4) "H(2|2|5), E(6|2|5), F(6|6|5)"$

(%i5) "b) Winkel ABF = beta"$

(%i6) "Vektor v_BA"$

(%i7) v_BA: transpose(matrix ([8.0,0.0,0.0])) - transpose(matrix ([8.0,8.0,0.0]));
                                   [  0.0  ]
                                   [       ]
(%o7)                              [ - 8.0 ]
                                   [       ]
                                   [  0.0  ]

(%i8) "Vektor v_BF"$

(%i9) v_BF: transpose(matrix ([6.0,6.0,5.0])) - transpose(matrix ([8.0,8.0,0.0]));
                                   [ - 2.0 ]
                                   [       ]
(%o9)                              [ - 2.0 ]
                                   [       ]
                                   [  5.0  ]

(%i10) "Winkel zwischen Vektor v_BA und Vektor v_BF: alpha =  69.625472811265\xef\xbe\xb0 "$

(%i11) "c) Schnitt der Diagonalen BH und DF"$

(%i12) "Zwei Punkte D, F der Gerade g"$

(%i13) D : transpose(matrix ([0.0,0.0,0.0]));
                                    [ 0.0 ]
                                    [     ]
(%o13)                              [ 0.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i14) F : transpose(matrix ([6.0,6.0,5.0]));
                                    [ 6.0 ]
                                    [     ]
(%o14)                              [ 6.0 ]
                                    [     ]
                                    [ 5.0 ]

(%i15) "Aufpunkt stuetzvec"$

(%i16) stuetzg_DF : transpose(matrix ([0.0,0.0,0.0]));
                                    [ 0.0 ]
                                    [     ]
(%o16)                              [ 0.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i17) "Richtungsvektor uvec"$

(%i18) uvecg_DF : B - A;
                                    [ 6.0 ]
                                    [     ]
(%o18)                              [ 6.0 ]
                                    [     ]
                                    [ 5.0 ]

(%i21) "Zwei Punkte B, F der Gerade g"$

(%i22) B : transpose(matrix ([8.0,8.0,0.0]));
                                    [ 8.0 ]
                                    [     ]
(%o22)                              [ 8.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i23) F : transpose(matrix ([2.0,2.0,5.0]));
                                    [ 2.0 ]
                                    [     ]
(%o23)                              [ 2.0 ]
                                    [     ]
                                    [ 5.0 ]

(%i24) "Aufpunkt stuetzvec"$

(%i25) stuetzg_BH : transpose(matrix ([8.0,8.0,0.0]));
                                    [ 8.0 ]
                                    [     ]
(%o25)                              [ 8.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i26) "Richtungsvektor uvec"$

(%i27) uvecg_BH : B - A;
                                   [ - 6.0 ]
                                   [       ]
(%o27)                             [ - 6.0 ]
                                   [       ]
                                   [  5.0  ]


(%i30) "Schnittpunkt der Geraden g_BH und g_DF"$

(%i31) sp : transpose(matrix([  4.000000000000,  4.000000000000,  3.333333333333]));
                              [      4.0       ]
                              [                ]
(%o31)                        [      4.0       ]
                              [                ]
                              [ 3.333333333333 ]

(%i32) "Schnittwinkel alpha =  61.017917732406"$

(%i33) "d) Oberflaecheninhalt = Grundseite unten + Grundseite oben + "$

(%i34) " Oberflaecheninhalt += 4 * Seitenflaeche "$

(%i35) "G_u = 8 * 8, G_o = 4 * 4 "$

(%i36) "S = A_Trapez = h * 0.5 * (AB + EF) = h * 0.5 * (8+4)"$

(%i37) "h = |M_AB,M_EF|, M_AB(8|4|0), M_EF(6|4|5)"$

(%i38) "Vektor v_M1M2"$

(%i39) v_M1M2: transpose(matrix ([6.0,4.0,5.0])) - transpose(matrix ([8.0,4.0,0.0]));
                                   [ - 2.0 ]
                                   [       ]
(%o39)                             [  0.0  ]
                                   [       ]
                                   [  5.0  ]

(%i40) "Länge l des Vektors v_M1M2: l = 5.38516480713"$

(%i41) "h = |M_AB,M_EF| = 5.38516480713"$

(%i42) O = 8*8 + 4*4 + 4*(0.5*12*5.38516480713);
(%o42)                        O = 209.24395537112

(%i43) "Oberflaeche O = 209.24395537112 FE"$

(%i44) S = (0.5*12*5.38516480713);
(%o44)                        S = 32.31098884278

(%i45) "Seitenflaeche S = 32.31098884278 FE"$