Question

Найдите площадь круга, описанного около правильного треугольника со стороной 9 см.

Answer 1

Найдите площадь круга, описанного около правильного треугольника со стороной 9 см.

Sкруга= πR²,  R=(2/3 )h, где h - высота правильного треугольника, около которого описана окружность.

h²=(3/4)a²=(3/4)·9²,  R²=(2/3 )²h²=(4/9)·(3/4)·9²=27, Sкруга= π27,
Sкруга= 27π,

Answer 2

Calculating the Area of a Circle Inscribed in a Right Triangle

To find the area of a circle inscribed in a right triangle with a side of 9 cm, we can use the formula for the radius of the inscribed circle, which is given by r = a / sqrt(3), where a is the length of the side of the triangle. In this case, a = 9 cm.

Using the formula, we can calculate the radius of the inscribed circle: r = 9 / sqrt(3) = 3 * sqrt(3) cm.

Now that we have the radius of the inscribed circle, we can calculate the area of the circle using the formula for the area of a circle, which is given by A = π * r^2.

Calculating the Area of the Circle

Using the radius we calculated earlier, the area of the circle can be found as follows: A = π * (3 * sqrt(3))^2 = 9π cm^2.

Therefore, the area of the circle inscribed in the right triangle with a side of 9 cm is 9π square centimeters.

Answer

The area of the circle is 9π square centimeters.