Area of parallelogram confusion

[quaint gazelle]

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[sweet walrus]

This is how I’ve drawn the parallelogram

For some reason the question has used the area of a triangle formula for the area of a parallelogram this has deeply confused me

[turbid needle]

The area of a parallelogram with sides a and b and angle γ is S = ab sin(γ).

[sweet walrus]

So you can basically just use the area of a triangle for the area of a parallelogram

[turbid needle]

Well, for the triangle we also have a factor of 1/2.

The area of a parallelogram is more fundamental, so to speak.

[sweet walrus]

OHHH right ! Yeah I get what you mean, so with the area of the triangle it'll be half of the parallelogram but since the area of a triangle has a half in it we divide the halfed area (50/2 =25) by a half (25/ 1/2 =50) to get 50 right ?

Oh wow this makes so much sense nos

now*

[turbid needle]

Yes.

Note that a similar approach works for a parallelepiped and a tetrahedron. The only difference is that their volumes differ by a factor of 1/6.

[sweet walrus]

Alrighty, well I'm gunna close the post now but thanks alot for your help !