Video Transcript
In the opposite figure, line 𝐴𝐵
is parallel to line 𝐶𝐹 and the distance between them is ℎ, where ℎ equals three
centimeters and 𝐴𝐵 equals four centimeters. Find the areas of parallelograms
𝐴𝐵𝐶𝐷 and 𝐴𝐵𝐸𝐹, respectively.
It might be useful to begin by
highlighting these two specific parallelograms. First, we have parallelogram
𝐴𝐵𝐶𝐷. And secondly, we have 𝐴𝐵𝐸𝐹. We can observe that both
parallelograms share the same side of 𝐴𝐵. The heights of both of these
parallelograms will be the distance between the parallel lines 𝐴𝐵 and 𝐶𝐹. This is also marked on the figure
with the letter ℎ. Because these parallelogram share
the same base 𝐴𝐵, we can use the property that parallelograms between a pair of
parallel lines have the same area when they share a common base. So 𝐴𝐵𝐶𝐷 and 𝐴𝐵𝐸𝐹 will
actually have the same area.
To find the area of either of these
parallelograms, we can use the formula that the area of a parallelogram is equal to
the base multiplied by the perpendicular height. To find the area of 𝐴𝐵𝐶𝐷, we
take the base, which is given as four centimeters, and multiply it by the
perpendicular height ℎ, which is given as three centimeters. This gives us an answer of 12
square centimeters. The area of parallelogram 𝐴𝐵𝐸𝐹
is also equal to 12 square centimeters. And so we have found the areas of
both parallelograms.
