How is the parallelogram area formula derived?

1, the area formula of parallelogram: base× height (excavation and filling method can be used, and the derivation method is shown in the figure); If "h" is used for height, "a" for base and "s" for parallelogram area, then s parallelogram = a * h.

2. The area of parallelogram is equal to the product of two adjacent sides multiplied by the sine value of the included angle; If "A" and "B" represent the lengths of two groups of adjacent sides, α represents the included angle between the two sides, and "S" represents the area of parallelogram, then S parallelogram = A "B * sin α.

Parallelogram is a closed figure composed of two groups of parallel lines on the same two-dimensional plane. Parallelogram is generally named by the graphic name followed by four vertices.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the diagonals of the parallelogram are equal. On the contrary, a quadrilateral with only one pair of parallel sides is a trapezoid.

Extended data

Reverse use of parallelogram area formula

1. Given the area and base of a parallelogram, find its height.

Height = area of parallelogram.

2. Know the area and height of the parallelogram and find the bottom.

Base = area/height of parallelogram

3. The base or height of parallelogram can be found by arithmetic method or equation.

4. The area relation of parallelogram with the same base and equal height.

The parallelogram with the same base and height has the same area.