Answer :
If the area of the pentagon is 36, then the area of the pentagon FGHIJ is 64.
What are Similar figures?
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
Given that the length of the side of the smaller pentagon is 12, while the length of the side of the larger pentagon is 16.
Since the two of the given figures are similar figures, therefore, we can write,
(Area of smaller pentagon)/(Area of larger pentagon) = (Ratio of the sides)²
(Area of pentagon ABCDE)/(Area of pentagon FGHIJ) = (AE / FJ)²
(36)/(Area of pentagon FGHIJ) = (12/16)²
Area of pentagon FGHIJ = 36 × (16/12)²
Area of pentagon FGHIJ = 36 × (256/144)
Area of pentagon FGHIJ = 64
Hence, the area of the pentagon FGHIJ is 64.
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