Question

A hexagon is inscribed inside a circle with the radius of 14√2 cm. Find the area of the region between the circle and hexagon.
1. 272 square cm
2. 214 square cm
3. 198 square cm
4. 158 square cm

Answer 1

Correct Answer - Option 2 : 214 square cm

Given:

A hexagon is inscribed inside a circle with the radius of 14√2 cm

Formula Used:

We know that

Area of circle = πr²

Area of hexagon = 6 × \(\frac{{\sqrt 3 }}{4}\) × (side) ²

Calculation:

A hexagon is inscribed inside a circle with the radius of 14√2 cm so the side of hexagon is equal to radius of circle

∴ Area of hexagon = 6 × \(\frac{{\sqrt 3 }}{4}\) × (14√2) ² ≈ 1018 square cm

Now, area of circle = πr² = π(14√2)² = 1232 square cm

We have to find the area of region between circle and hexagon

∴ Area of region = 1232 – 1018 = 214 square cm