A hexagon inscribed in a circle is a hexagon so placed within the circle that its six vertices touch the circumference. In such a situation, the circle circumscribes or restricts the hexagon within its limit of circumference. A circle can only circumscribe a regular hexagon. Let us see the diagram of a regular hexagon inscribed in a circle.

How to Inscribe a Hexagon in a Circle

Let us learn how to construct a regular hexagon inscribed in a circle. Given below is a link showing how to inscribe a hexagon in a circle.

Solved Examples

Finding Area

Finding the area of a hexagon inscribed in a circle when RADIUS of CIRCLE is known

If a regular hexagon is inscribed in a circle with a radius of 4 cm, what is the area of the hexagon?

Solution:

As we know, Side (s) of a hexagon inscribed in a circle = radius (r) of circumscribed circle Thus, Area (A) = 3√3/2 × (r)^{2} , here r = 4 cm = 3√3/2 × 4 × 4 = 24√3 sq. cm

Finding Perimeter

Finding the perimeter of a hexagon inscribed in a circle when RADIUS of CIRCLE is known

Find the perimeter of a hexagon inscribed in a circle with radius 6 cm.

Solution:

As we know, Side (s) of a hexagon inscribed in a circle = radius (r) of circumscribed circle Perimeter (P) = 6r, here r = 6 cm = 6 × 6 = 36 cm