Answer:
The area of the larger hexagon is 196 in²
Step-by-step explanation:
Area of a regular hexagon is given as;
[tex]A = (\frac{3\sqrt{3} }{2} )a^2[/tex]
where;
a is side of the hexagon
Given the area of the smaller hexagon as 36in², we now determine the side of this smaller hexagon.
[tex]A = (\frac{3\sqrt{3} }{2} )a^2[/tex]
A = (2.59808)a²
a² = A / (2.59808)
a² = 36in² / (2.59808)
a² = 13.8564 in²
a = √ 13.8564 in²
a = 3.7224 in
let the side of the larger hexagon = b
Given the ratio of the sides of small to large hexagon as 3:7,
a:b = 3:7
[tex]\frac{a}{b} = \frac{3}{7} \\\\\frac{3.7224}{b} = \frac{3}{7} \\\\b = \frac{3.7224*7}{3} = 8.6856 \ in[/tex]
Now, with the side of the larger hexagon known, we calculate its area.
A = (2.59808)b²
A = (2.59808)(8.6856)²
A = 196 in²
Therefore, the area of the larger hexagon is 196 in²
