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Sagot :
Answer
Explanation
The area of the hexagon is given as
[tex]\text{Area of the hexagon = }\frac{3\sqrt[]{3}}{2}a^2[/tex]where
a = side of the hexagon, which is the radius of the circle in the image.
Area of the hexagon = 40.8 square inches
[tex]\begin{gathered} \text{Area of the hexagon = }\frac{3\sqrt[]{3}}{2}a^2 \\ 40.8=\frac{3\sqrt[]{3}}{2}a^2 \\ a^2=\frac{2\times40.8}{3\sqrt[]{3}} \\ a^2=15.704 \\ \text{Take the square root of both sides} \\ a=3.96\text{ inches} \end{gathered}[/tex]Since the pink area is attached to the hexagon, we can easily calculate its area by noting that it is a sector of a circle with angle of one interior side of the hexagon subtended at the center of the circle.
One interior angle of a haxagon = 120°
Area of a sector is given as
[tex]\text{Area of a sector = }\frac{\theta}{360\degree}\times\pi r^2[/tex]where
θ = Angle subtended by the sector at the center of the circle = 120°
π = pi = 3.14
r = radius of the circle = length of a side of the hexagon = 3.96 inches
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