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Answer :
The area of the smaller pentagon is 6 in²
How to determine the area of the smaller pentagon?
The attached figure represents the missing piece of the question
The ratio of the side lengths are given as:
Small : Large = 2.5 : 7.5
The area of the larger pentagon is given as:
Area = 54 in²
Using the given parameters, the area of the small pentagon is:
Area = (Small/Large)² * Area of Large
This gives
Area = (2.5/7.5)² * 54
Evaluate
Area = 6
Hence, the area of the smaller pentagon is 6 in²
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