Video Transcript
Find an expression for the area of
the parallelogram.
In this question, we are asked to
find an expression for the area of a given parallelogram. To do this, we first need to recall
that the area of a parallelogram is given by the length of the base of the
parallelogram multiplied by its perpendicular height.
We are given the length of the side
𝐶𝐷 in the figure. So, we will choose this as the base
of our parallelogram. Its length is 𝑥 squared plus three
𝑥. The perpendicular height of the
parallelogram is then the perpendicular distance between the sides 𝐶𝐷 and
𝐴𝐵. Since there is a right angle at 𝐸,
we can see that this is given by the length of 𝐷𝐸, which is two 𝑥. Therefore, we can multiply these
expressions to find an expression for the area of the parallelogram.
We have that the area is given by
𝑥 squared plus three 𝑥 multiplied by two 𝑥. We can simplify this expression for
the area by distributing the monomial factor over the parentheses. To do this, we need to multiply
each term inside the parentheses by the monomial factor. We obtain two 𝑥 times 𝑥 squared
plus two 𝑥 times three 𝑥. We can then simplify this
expression by recalling that 𝑥 times 𝑥 squared is 𝑥 cubed and 𝑥 times 𝑥 is 𝑥
squared. We have that the area of the
parallelogram is given by two 𝑥 cubed plus six 𝑥 squared.
