The area of twenty-four gons is 8 pi, and the area of the inscribed circle is 2 pi. find the perimeter of 24 squares.

Since we know that the area of a 24-gon is 8n sq. units, and the area of the circle inscribed in it is 2p sq. units.

We can split a quadrilateral into 24 triangles.

Let’s write the area of 24 gons as:

S24 = 24 * S triangle = 8п;

Hence S of the triangle = 8n / 24 = n / 3 = 1/2 * a24 * r.

a24 = 2п / 3r.

The area of the inscribed circle is S = nr ^ 2 = 2п;

r ^ 2 = 2;

r = √2.

It remains to find the perimeter of the 24 – x gon:

P24 = 24 * a24 = 24 * 2п / 3r = 16п / √2 = 8√2 * п.

Answer: P24 = 8√2 * п.