Question

В правильный треугольник вписана окружность радиуса 3 см. Найдите площадь треугольника.

Answer 1

Ответ:

радиус вписанной окружности : r=a√3/6

3=a√3/6

a√3=3*6

a√3=18

a=18/√3

a=6√3

площадь равностороннего треугольника:

S=a^2*√3/4

S=108√3/4

S=27√3 см^2

Ответ: S=27√3 см^2

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Answer 2

Finding the Area of a Triangle Inscribed in a Circle

To find the area of a triangle inscribed in a circle, we need to know the radius of the circle. In this case, the radius of the circle is given as 3 cm.

The area of a triangle can be calculated using the formula: Area = (base * height) / 2. However, in this case, we don't have the base and height of the triangle directly given.

To find the base and height of the triangle, we can use the fact that the radius of the circle is perpendicular to the sides of the triangle at the points of tangency. This means that the radius of the circle is also the height of the triangle.

Since the radius of the circle is given as 3 cm, we can use this as the height of the triangle.

To find the base of the triangle, we can use the formula for the circumference of a circle: Circumference = 2 * π * radius. In this case, the radius is given as 3 cm, so the circumference of the circle is Circumference = 2 * π * 3 = 6π cm.

Since the base of the triangle is equal to the circumference of the circle, the base of the triangle is 6π cm.

Now, we can calculate the area of the triangle using the formula: Area = (base * height) / 2.

Substituting the values, we get:

Area = (6π * 3) / 2 = 9π cm².

Therefore, the area of the triangle inscribed in the circle with a radius of 3 cm is 9π cm².