Question

A regular hexagon is inscribed in a circle of radius 14cm .Find the area of region between the circle and the hexagon [√3=1.732,π=22/7]

Answer 1

Answer:

Step-by-step explanation:

A regular hexagon is made up of 6 equilateral Triangles.

The distance from the vertex to the center equals to the radius of the circle and equals to the sides of the hexagon.

The hexagon is Therefore of side 14cm.

To get the area of the region between the circle and the hexagon we need to get the area of the circle and the area of the hexagon.

To get the area of the hexagon we need to get the height of the equilateral triangles.

By pythagoras theorem we can get this.

h =√ 14² - (14/2)²

h = √147 = 12.12 cm

Area of a triangle = 1/2 × height × base

= 1/2 × 14 × 12.12 = 84.84

For the hexagon = 6 × 84.84 = 509.04 cm²

For the circle = πr²

= 22/7 × 14² = 616 cm²

Area of the region = 616 - 509.04 = 106.96 cm²