Question

знайти площу круга, вписаного в рівносторонній трикутник, площа якого дорівнює 9√3 см²​... Геометрія 9 клас​

Answer 1

Ответ:

Объяснение: S₃=9√3, S₃=a²√3/4, значит а²√3/4=9√3 ⇒а²=36, а=6.

r=a√3/6, т.е.  r=6√3/6=√3.

S(вп. круга)=πr²=π(√3)²=3π.

Answer 2

Finding the Area of a Circle Inscribed in an Equilateral Triangle

To find the area of a circle inscribed in an equilateral triangle, we can use the formula for the area of an equilateral triangle and the properties of a circle inscribed in it.

Step 1: Finding the Radius of the Inscribed Circle

The radius of the inscribed circle in an equilateral triangle can be found using the formula:

radius = (side length of the equilateral triangle) / (2 * √3)

Given that the area of the equilateral triangle is 9√3 cm², we can find the side length of the equilateral triangle using the formula:

area = (√3 / 4) * (side length)²

Solving for the side length, we get:

side length = 2 * √(area / √3)

Substituting the given area (9√3 cm²) into the formula, we can find the side length of the equilateral triangle.

Step 2: Calculating the Area of the Inscribed Circle

Once we have the side length of the equilateral triangle, we can use it to find the radius of the inscribed circle. Then, we can use the formula for the area of a circle:

area = π * (radius)²

Substitute the radius we found into this formula to calculate the area of the inscribed circle.

Let's proceed with these calculations.