How do you calculate the area of a parallelogram from vectors?
Quick Answer
To calculate the area of a parallelogram from vectors, find the cross product of the sides and vectors. The area equals the length of the cross product of two vectors.
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- Cut the parallelogram in half
Create a triangle shape from the parallelogram by drawing a diagonal line down the middle of the original shape.
- Find the vertices
Write down the points on the plot where the three corners of the triangle meet. These are the vertices.
- Create the area equation
Add the first plot point to the second plot point to solve for the u variable. Add the first plot point to the third plot point to solve for the v variable. The area of the triangle equals v * u.
- Find the absolute matrix value
Replace the third-dimension plot point with zero. Create a matrix of the v and u plot points. Find the absolute value by cross multiplying the matrix numbers. Write down the resulting three-figure plot point.
- Solve the equation
Write the equation as area = 1/2 x the square root of p1 ^ 2 x p2 ^ 2 x p3 ^2. Replace each p with a plot point. Take each of the three plot points to the second power. Multiply the plot points together, and find the square root of the result. Multiply this number by half to solve for the area of the parallelogram.
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