Answer:
242 in²
Step-by-step explanation:
Let's denote the height of the parallelogram as [tex] h [/tex] and the base as [tex] b [/tex].
Given:
Height [tex] h = 22 [/tex] inches
Base [tex] b [/tex] is one half of the height [tex] h [/tex].
So [tex] b = \dfrac{1}{2}h [/tex]
We know that the area [tex] A [/tex] of a parallelogram is given by the formula:
[tex] \Large\boxed{\boxed{\sf Area = \textsf{base} \times \textsf{height}}} [/tex]
Substitute the values we have:
[tex] A = b \times h [/tex]
[tex] A = \left(\dfrac{1}{2}h\right) \times h [/tex]
[tex] A = \dfrac{1}{2}h^2 [/tex]
Now, substitute [tex] h = 22 [/tex] inches into the formula:
[tex] A = \dfrac{1}{2}(22)^2 [/tex]
[tex] A = \dfrac{1}{2} \times 484 [/tex]
[tex] A = 242 \textsf{inches}^2 [/tex]
So, the area of the parallelogram is 242 in².
