Answer: 38 inches
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How I got the answer:
The bottom base is 10 inches, so the top parallel side is also 10 inches. Parallelograms have congruent opposite sides that are parallel.
The left slanted exterior side is 9 inches, so the same applies to the right slanted side as well.
We have the four sides: 9, 10, 9, 10
They add up to 9+10+9+10 = 19+19 = 38 which is the perimeter we want
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You can use the formula
P = 2*(s1+s2)
where
P = perimeter
s1 and s2 are the two different outer sides of the parallelogram. In this case, s1 = 9 and s2 = 10.
Notice how I did not use the 8 inch segment at all. The interior side is not included when we talk about the perimeter. We only want the distance around the outer edge. Think of it like trying to find out how much fencing we'll need to surround the parking lot (and we don't want to subdivide or cut into the parking lot with fencing).