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"The Area of a Parallelogram" Calculation of the Area of a Polygon PPT Courseware 3
group discussion:
① Compared with the original parallelogram, has the area of the rectangle changed?
②What is the relationship between the length and width of the assembled rectangle and the base and height of the original parallelogram?
③Can the formula for calculating the area of a parallelogram be derived from the formula for calculating the area of a rectangle?
We convert a parallelogram into a rectangle whose area is equal to the area of the original parallelogram. The length of this rectangle is equal to the base of the parallelogram, and the width of this rectangle is equal to the height of the parallelogram. Because the area of the rectangle = length × width, the area of the parallelogram = base × height.
If S represents the area of the parallelogram, a represents the base of the parallelogram, and h represents the height of the parallelogram, then the formula for the area of the parallelogram is...
S=ah
By cutting and piecing together, we can clearly see that a parallelogram can be converted into a rectangle. The area of the converted rectangle is equal to the area of the original parallelogram, and the length of the rectangle is equal to the base of the parallelogram, and the width of the rectangle is equal to the parallelogram. The heights of the quadrilaterals are equal.
Area of rectangle = length × width
Area of parallelogram = base × height
S=a×h
It can also be written as: S＝a·h or S＝ah
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