Video Transcript
In the opposite figure, line 𝐴𝐵
is parallel to line 𝐸𝐷 and line segment 𝐴𝐶 is parallel to line segment 𝐵𝐷. If the area of triangle 𝐴𝐵𝐸
equals seven square centimeters, find the area of parallelogram 𝐴𝐵𝐷𝐶.
We can observe here that since the
two lines 𝐴𝐵 and 𝐸𝐷 are parallel and the two line segments 𝐴𝐶 and 𝐵𝐷 are
parallel, then we have indeed got a parallelogram in 𝐴𝐵𝐷𝐶. Given that the area of triangle
𝐴𝐵𝐸 is seven square centimeters, we need to work out the area of parallelogram
𝐴𝐵𝐷𝐶. To do this, we can use the fact
that the triangle and the parallelogram share the same base of 𝐴𝐵. Importantly, they also share the
same perpendicular height, which we can define with the letter ℎ.
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 𝐴𝐵𝐸 is
equal to one-half multiplied by the length of the line segment 𝐴𝐵 multiplied by
ℎ. 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 𝐴𝐵𝐷𝐶 can be calculated by the length of 𝐴𝐵 multiplied by ℎ.
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 𝐴𝐵𝐸 is seven square centimeters, we double it, giving us the answer that
the area of parallelogram 𝐴𝐵𝐷𝐶 is 14 square centimeters.
