The area of the larger hexagon is 1126.74 ft²
Explanation:
Given:
Ratio of sides of two hexagons = 7 : 4
Area of the smaller hexagon = 368 ft²
Area of the larger hexagon = ?
We know:
Area of hexagon = [tex]\frac{3\sqrt{3} }{2} a^2[/tex]
where,
a = side of the hexagon
According to the question:
[tex]368 = \frac{3\sqrt{3} a^2}{2} \\\\a^2 = \frac{368X 2}{3\sqrt{3} } \\\\a^2 = 141.64\\\\a = 11.9[/tex]
Therefore, the side of smaller hexagon is 11.9
So,
[tex]\frac{7}{4} = \frac{x}{11.9} \\\\x = 20.825[/tex]
Therefore, the length of larger hexagon is 20.825
Area of larger hexagon = [tex]\frac{3\sqrt{3}(x)^2 }{2}[/tex]
= [tex]\frac{3X\sqrt{3} (20.825)^2}{2}[/tex]
= 1126.74 ft²
Therefore, the area of the larger hexagon is 1126.74 ft²
