The sides of the rectangle are 8 and 6. Find the radius of the circle around this rectangle.

The radius of the circle into which the rectangle is inscribed is equal to half the diagonal of this rectangle.

Let us define, by the Pythagorean theorem, the AC diagonal. AC ^ 2 = AB ^ 2 + BC ^ 2 = 36 + 64 = 100.

AC = 10 cm, then R = OA = AC / 2 = 10/2 = 5 cm.

Answer: The radius of the circumscribed circle is 5 cm.

Let’s define the area of the square. Sq = 8 * 8 = 64 cm2.

Determine the area of the cut rectangle Sпр = 3 * 2 = 6 cm2.

Then the area of the remaining figure is equal to: S = Sq – Spr = 64 – 6 = 58 cm2.

Answer: The area of the remaining part is 58 cm2.