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Volume of tetrahedron = 1/3 (base area) (height) Volume of parallelopiped = (base area) (height) They have same heights, but the base area of the tetrahedron is half of that of the …
area of base of parallelepiped (parallelogram) = b ×c. the vector b ×c will be perpendicular to base. therefore: volume of parallelopiped = area of base × height = (b ×c) × A cos θ = a ⋅ (b ×c) …
$\begingroup$ @user3180 The argument is complete: if we accept that 1) For a cuboid the volume is given by the (absolute value) of the determinant of the corresponding diagonal …
Volume of a n dimensional parallelepiped in n dimensional space is given by the determinant of the n by n matrix formed by it's edge vectors. Which makes sense considering that unit axis …
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