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Hi there! My question involves the area of a parallelogram. Now, I know how to prove the commonly used formula (b*h) very easily, however, there is a formula given on Wikipedia as an alternative that states....Given two sides B and C with angle (theta), B*C*sin(theta)=Area of a parallelogram. Now the problem is that there is no proof given for this problem and I keep coming up with contradictions in my head. For example, say you start with a rectangle with sides A and B where A does not equal B. Now, take that rectangle and move two of it's angles that are collinear(lie on the same side or line) through an equivalent angle (theta). What you will be left with is a parallelogram whose sides are the same length as the rectangle we started with (A and B). We know that the rectangle has an area of A*B, so it should be safe to assume that the parallelogram has the same area. This is where the trouble comes in (in my head at least). The definition given in Wikipedia states that the area of a parallelogram with two sides A and B and an angle theta is equal to A*B*sin(theta). So, my questions to you is, where is my sin(theta) missing? What mistake(s) have I made? Have there been any incorrect assumptions I have made? Does anyone know a proof for the formula given on Wikipedia? For all those who help me in understanding and using there time to help me out, thank you in advance!

(Image below to describe my reasoning.)

(Image below to describe my reasoning.)

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