how is the size of a parallelogram related to the size of to trapezoid
The size of a parallelogram and a trapezoid refers to their respective areas. These two shapes are different, so their sizes are not directly related in a simple way.
To understand the relationship between the size of a parallelogram and a trapezoid, we need to compare their formulas for calculating the area.
The formula for the area of a parallelogram is:
Area = base × height
The formula for the area of a trapezoid is:
Area = (base1 + base2) / 2 × height
In a parallelogram, the base and the height are perpendicular to each other. The base is any of the parallel sides, and the height is the perpendicular distance between those parallel sides.
On the other hand, a trapezoid has two parallel sides (base1 and base2) and two non-parallel sides. The height is again the perpendicular distance between the two parallel sides.
So, in general, the size (area) of a trapezoid will be larger than that of a parallelogram, given the same values for base and height. This is because the formula for the area of a trapezoid involves averaging the lengths of the two parallel sides, whereas the formula for a parallelogram directly multiplies the base and height.
However, it's important to note that the actual relationship between the size of a specific parallelogram and a trapezoid will depend on the specific measurements of their bases and heights.