In an isosceles triangle, the base and height are equal to 4. Find the area of the circle around this triangle.

Since the triangle ABC is isosceles, then its height BH is also its median, then AH = CH = AC / 2 = 4/2 = 2 cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, AB ^ 2 = AH ^ 2 + BH ^ 2 = 4 + 16 = 20.

AB = BC = 2 * √5 cm.

Let’s define the area of the triangle ABC.

Savs = AC * ВН / 2 = 4 * 4/2 = 8 cm2.

The radius of the circumscribed circle is: R = AB * BC * AC / 4 * Savs = 2 * √5 * 2 * √5 * 4/4 * 8 = 2.5 cm.

Then the area of the circle is: S = π * R2 = 6.25 * π cm2.

Answer: The area of the circumscribed circle is 6.25 * π cm2.