### Video Transcript

In the figure below, line π΄π΅ is
parallel to line πΆπΈ, line segment π΄πΆ is parallel to line segment π΅π·, and
π΄π΅πΈπΉ is a rectangle. If π΅πΈ equals four centimeters and
π΄π΅ equals three centimeters, find the area of parallelogram π΄π΅π·πΆ.

From the information that we are
given, we note that we have two pairs of parallel lines, which confirms that
π΄π΅π·πΆ is indeed a parallelogram. We are further told that π΄π΅πΈπΉ
is a rectangle. Since a rectangle is simply a
special case of parallelogram, it means we can also note that the line segments π΄πΉ
and π΅πΈ are also parallel. We can use the information about
π΄π΅πΈπΉ to help us work out the area of the parallelogram π΄π΅π·πΆ. We can use the information that
π΅πΈ is equal to four centimeters and π΄π΅ is equal to three centimeters to help us
work out the area of the rectangle π΄π΅πΈπΉ.

If youβre not sure why this is
useful, letβs recall an important property about parallelograms created between two
parallel lines. Parallelograms between a pair of
parallel lines with congruent bases have the same area, so even though π΄π΅πΈπΉ is a
rectangle, thatβs a special type of parallelogram, and the line segment π΄π΅ is a
common side to both π΄π΅πΈπΉ and π΄π΅π·πΆ. So if we work out the area of
π΄π΅πΈπΉ, itβs going to be the same as the area of π΄π΅π·πΆ.

And of course, to work out the area
of a rectangle, we multiply the length by the width. Three times four is 12, and the
area units will be square centimeters. The area of π΄π΅π·πΆ is going to be
equal to this. So itβs also 12 square
centimeters. We could also have worked out the
area of π΄π΅π·πΆ directly. The area of a parallelogram is
found by multiplying the base by the perpendicular height. The base of π΄π΅π·πΆ is three
centimeters, and the perpendicular height is also the length of the line segment
π΅πΈ, which is four centimeters. Either method would produce the
result that the area of π΄π΅π·πΆ is 12 square centimeters.