Question

GH= 3.4 inches and the area of the hexagon is 40.8 inches squared.

Answer 1

Step-by-step explanation

The area of the hexagon is given as

`\text{Area of the hexagon = }\frac{3\sqrt[]{3}}{2}a^2`

where

a = side of the hexagon, which is the radius of the circle in the image.

Area of the hexagon = 40.8 square inches

`\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*40.8}{3\sqrt[]{3}} \\ a^2=15.704 \\ \text{Take the square root of both sides} \\ a=3.96\text{ inches} \end{gathered}`

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

`\text{Area of a sector = }(\theta)/(360\degree)*\pi r^2`

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