What is the formula of all parallelograms ? Explain your answer

Answer 1

It seems like you might be asking for the area formula for parallelograms. The general formula to calculate the area (A) of a parallelogram is:

\[ A = base \times height \]

Where:
- The base (b) is the length of one of the sides of the parallelogram.
- The height (h) is the perpendicular distance from the base to the opposite side (not the slant height).

The reason this formula works is that if you were to take a right triangle from one side of the parallelogram and move it to the other side, you would end up with a rectangle. The base and the height dimensions of this rectangle would be the same as the original parallelogram, and since the area of a rectangle is found by multiplying the base by the height, the same formula applies to parallelograms as well.

If you are asking for general properties or other formulas relevant to parallelograms, here are a few key characteristics:
- Opposite sides are equal in length: If a parallelogram has sides a and b, then the formula expressing the relationship between the sides would be a = c and b = d, where c and d are the lengths of the opposite sides, respectively.
- Opposite angles are equal: If a parallelogram has angles A, B, C, and D, then A = C and B = D.
- Adjacent angles are supplementary: A + B = B + C = C + D = D + A = 180 degrees.
- Diagonals of a parallelogram bisect each other: This means that if two diagonals intersect each other, they will divide each other into two equal parts.

Please let me know if you need information beyond the area formula or if you were referring to a different "formula" related to parallelograms.