### Video Transcript

In the opposite figure, line π΄π΅
is parallel to line πΈπ· and line segment π΄πΆ is parallel to line segment π΅π·. If the area of triangle π΄π΅πΈ
equals seven square centimeters, find the area of parallelogram π΄π΅π·πΆ.

We can observe here that since the
two lines π΄π΅ and πΈπ· are parallel and the two line segments π΄πΆ and π΅π· are
parallel, then we have indeed got a parallelogram in π΄π΅π·πΆ. Given that the area of triangle
π΄π΅πΈ is seven square centimeters, we need to work out the area of parallelogram
π΄π΅π·πΆ. To do this, we can use the fact
that the triangle and the parallelogram share the same base of π΄π΅. Importantly, they also share the
same perpendicular height, which we can define with the letter β.

Now to find the area of a triangle,
we recall that this is equal to one-half multiplied by the base multiplied by the
perpendicular height. So the area of triangle π΄π΅πΈ is
equal to one-half multiplied by the length of the line segment π΄π΅ multiplied by
β. Equally, we can recall that to find
the area of a parallelogram, we multiply the base by the perpendicular height. Therefore, the area of
parallelogram π΄π΅π·πΆ can be calculated by the length of π΄π΅ multiplied by β.

If we then observe the right-hand
side of both of these equations, we can observe that the parallelogram is simply
double the area of the triangle. Therefore, given that the area of
triangle π΄π΅πΈ is seven square centimeters, we double it, giving us the answer that
the area of parallelogram π΄π΅π·πΆ is 14 square centimeters.