The ratio of the side lengths of two regular hexagons is 3 to 7. If the area of the smaller hexagon is 18 square units, then the area of the larger hexagon is ________.
Answer (2)
s i d e 2 s i d e 1 = 7 3 A re a 2 A re a 1 = ( 7 3 ) 2 = 49 9 A re a 2 18 = 49 9 cross m u lt i pl y 9 A re a 2 = 18 ⋅ 49 A re a 2 = 9 18 ⋅ 49 A re a 2 = 2 ⋅ 49 A re a 2 = 98
The area of the larger hexagon is 98 square units, calculated using the ratio of the side lengths and the properties of similar shapes. The area scales with the square of the ratio of the side lengths, leading to the final calculation. Therefore, using the known area of the smaller hexagon, we found the area of the larger hexagon by applying the ratio correctly.
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