why do the parallelogram and the rectangle have the same formula? b*h
Because that is the area of each.
thats all ..it seems so simple thank you
The formula for the area of a parallelogram is indeed given by the product of its base and height, just like a rectangle. This is because both a parallelogram and a rectangle have pairs of opposite sides that are parallel to each other.
To understand why this formula applies to both shapes, let's consider the properties of a parallelogram and a rectangle:
1. Parallelogram:
- A parallelogram has two sets of parallel sides.
- The opposite sides of a parallelogram have the same length.
- The height of a parallelogram is the perpendicular distance between its parallel sides.
2. Rectangle:
- A rectangle is a specific type of parallelogram where all angles are right angles.
- The opposite sides of a rectangle have the same length.
- The height of a rectangle is the perpendicular distance between its parallel sides.
Now, let's derive the formula for the area of a parallelogram:
The area of a parallelogram can be computed as the base multiplied by the height. The base can be any of its sides, as long as the corresponding height is measured perpendicularly to that base. Since the opposite sides of a parallelogram have the same length, we can choose any of these sides as the base.
Now, let's relate this to a rectangle:
A rectangle is a special case of a parallelogram, where all angles are right angles. In a rectangle, the base and height run parallel to the sides of the rectangle. Therefore, they can be interchanged without affecting the calculation of the area.
Since the length of the base is the same as the length of one side of the rectangle and the height is the same as the length of the other side, the formula for the area of a rectangle (base multiplied by height) is the same as the formula for the area of a parallelogram.
In summary, the formula for the area of both a parallelogram and a rectangle is simply the product of the base and height because of their shared characteristics of having opposite sides that are parallel.