How to calculate the parallelogram area?

Description:

(1) 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 the 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

Extended data:

Parallelogram attributes (rectangle, diamond and square are all special parallelograms. )

(1) If a quadrilateral is a parallelogram, then two opposite sides of the quadrilateral are equal.

(Simply stated as "two opposite sides of a parallelogram are equal")

(2) If the quadrilateral is a parallelogram, then the two opposite corners of the quadrilateral are equal respectively.

(Simply stated as "the two diagonal lines of the parallelogram are equal respectively"? )

(3) If a quadrilateral is a parallelogram, then the adjacent angles of this quadrilateral are complementary.

(simply described as "complementary adjacent angles of parallelogram")

(4) The parallel height between two parallel lines is equal. (abbreviation of "the height and distance between parallel lines are equal everywhere")

(5) If a quadrilateral is a parallelogram, then the two diagonals of this quadrilateral are equally divided.

(short for "the diagonal of a parallelogram is divided equally")

(6) The figure obtained by connecting the midpoints of any quadrilateral side is a parallelogram. (inference)

(7) The area of a parallelogram is equal to the product of the base and the height. (It can be regarded as a rectangle. )

(8) Divide the parallelogram into two congruent parts by the straight line at the diagonal intersection of the parallelogram.

(9) A parallelogram is a central symmetric figure, and the center of symmetry is the intersection of two diagonals.

(10) The parallelogram is not an axisymmetric figure, but it is a centrally symmetric figure. Rectangles and diamonds are axisymmetric figures. Note: Square, rectangle and diamond are also special parallelograms, and they have the properties of parallelograms.

In (1 1) parallelogram ABCD (as shown in the figure), if E is the midpoint of AB, then AC and DE are equally divided. Generally speaking, if E is the bisector of N near A on AB, then AC and DE are bisectors (n+ 1).

(12) In the parallelogram ABCD, if AC and BD are diagonals of the parallelogram ABCD, the sum of squares of the four sides is equal to the sum of squares of the diagonals.

(13) The diagonal of the parallelogram divides the area of the parallelogram into four equal parts.

(14) In a parallelogram, the included angle formed by the heights of two different opposite sides, the smaller angle is equal to the smaller angle in the parallelogram, and the larger angle is equal to the larger angle in the parallelogram.

(15) The area of a parallelogram is equal to the product of the sine of the included angle between two adjacent sides.

References:

Parallelogram Baidu encyclopedia