A square with a side of 8 cm is described around a circle. Find the area of a 30-degree acute-angled triangle inscribed in a given circle.

1.The diameter of the circle will be equal to the side of the square-8, and the radius to half-4
2. The hypotenuse of a right-angled triangle inscribed in a circle is ALWAYS equal to the diameter-8
3.The side opposite an angle of 30 ° is equal to half of the hypotenuse-4
4.By the Pythagorean theorem, we find the 3rd side of the triangle
8 ^ 2 = 4 ^ 2 + x ^ 2
x ^ 2 = 64-16
x = 4 √3
5. Find the area of the triangle:
1/2 × 4 × 4√3 = 8 √3