It is easy to calculate its volume using the volume formula:
My current question is whetherIs there is any otheranother method to calculate the volume of the regular quadrilateral prism based on the known conditions in the software and the graph.? That is to say, for any drawn spatial geometry, what method is there to calculate their volume?
Draw the graph of the pyramid according to the following code:
Clear["Global`*"];
a = {Sqrt[2], 0, 0};
b = {0, Sqrt[2], 0};
c = -a;
d = -b;
o = Mean[{a, b, c, d}]
h = Sqrt[6]/2;
a1 = {Sqrt[2]/2, 0, h};
b1 = {0, Sqrt[2]/2, h};
c1 = {-Sqrt[2]/2, 0, h};
d1 = {0, -Sqrt[2]/2, h};
o1 = Mean[{a1, b1, c1, d1}]
labels = {Text[Style[O, 12, FontFamily -> "Times"], o, {-1, -1}],
Text[Style[O1, 12, FontFamily -> "Times"], o1, {-1, -1}],
Text[Style[A, 12, FontFamily -> "Times"], a, {-1, -1}],
Text[Style[B, 12, FontFamily -> "Times"], b, {1, 1}],
Text[Style[C, 12, FontFamily -> "Times"], c, {1, 1}],
Text[Style[D, 12, FontFamily -> "Times"], d, {-2, 0}],
Text[Style[A1, 12, FontFamily -> "Times"], a1, {3, 0}],
Text[Style[B1, 12, FontFamily -> "Times"], b1, {-1, -2}],
Text[Style[C1, 12, FontFamily -> "Times"], c1, {0, 1}],
Text[Style[D1, 12, FontFamily -> "Times"], d1, {3, 0}]};
dashLines = {Dashed,
AbsoluteThickness[2], {Line[{{o, o1}, {d, d1}}]}, {Red,
Line[{{c, d}, {a, d}, {b, d}, {a, c}}]}};
realLines = {AbsoluteThickness[2],
Line[{{a, b}, {b, b1}, {a1, a}, {b, b1}, {b1, a1}, {c, c1}, {b1,
c1}, {c1, d1}, {b, c}, {a1, c1}, {b1, d1}, {a1, d1}}]};
Show[Graphics3D[{dashLines, realLines, labels}, Boxed -> False,
ViewPoint -> {2, 3.5, 1.28}],
Graphics3D[{Arrow[{{o1 - o, o1 - o + {0, 0, 1}}, {a - o,
a - o + {1, 0, 0}}, {b - o, b - o + {0, 1, 0}}}],
Text[Style["z", 20, Italic, FontFamily -> "Times"],
o1 - o + {0, 0, 1}, {-1, -1}],
Text[Style["y", 20, Italic, FontFamily -> "Times"],
b - o + {0, 1, 0}, {-2, -1}],
Text[Style["x", 20, Italic, FontFamily -> "Times"],
a - o + {1, 0, 0}, {2, -1}]}]]
