Question

Find the area of the region between a regular hexagon with sides of 6" and its inscribed circle.

Answer 1

Answer:

Area of the region = 15.03 in²

Step-by-step explanation:

Area of region between a regular hexagon with sides 6" and circle inscribed.

So Area of region = Area of regular hexagon - area of circle

Now area of regular hexagon = $\frac{3a^{2} \sqrt{3}}{2}$

where a = side of the hexagon = 6"

Now area of regular hexagon = $\frac{3(6^{2})\sqrt{3}}{2}=\frac{108\sqrt{3}}{2}$ = 93.53 square in.

Area of circle inscribed = πr²

Here r is the radius of the circle = $\sqrt{6^{2}-3^{2}}=\sqrt{36-9}$

r = 5"

So area of the inscribed circle = π(5)² = 3.14(25) = 78.5 square in.

Now area of region = 93.53 - 78.5 = 15.03 in²