Question

Знайдіть площу круга вписаного в трикутник зі сторонами 3см, 5см, 6см​

Answer 1

Ответ:

Объяснение:

Фото

Answer 2

Finding the Area of a Circle Inscribed in a Triangle

To find the area of a circle inscribed in a triangle, we can use the formula:

Area of the circle = (s * r) / 2

where: - s is the semi-perimeter of the triangle, which is half the sum of the triangle's three sides. - r is the radius of the inscribed circle.

In this case, the triangle has sides measuring 3 cm, 5 cm, and 6 cm. Let's calculate the area of the circle inscribed in this triangle.

Calculating the Semi-Perimeter

To calculate the semi-perimeter (s), we need to find the sum of the triangle's three sides and divide it by 2.

s = (3 + 5 + 6) / 2 = 14 / 2 = 7 cm

Calculating the Radius

To find the radius (r) of the inscribed circle, we can use the formula:

r = (Area of the triangle) / s

The area of the triangle can be calculated using Heron's formula:

Area of the triangle = sqrt(s * (s - a) * (s - b) * (s - c))

where a, b, and c are the lengths of the triangle's sides.

In this case, a = 3 cm, b = 5 cm, and c = 6 cm.

Let's calculate the area of the triangle first:

Area of the triangle = sqrt(7 * (7 - 3) * (7 - 5) * (7 - 6)) = sqrt(7 * 4 * 2 * 1) = sqrt(56) cm²

Now, we can calculate the radius of the inscribed circle:

r = (sqrt(56) cm²) / 7 cm = sqrt(8) cm ≈ 2.83 cm

Calculating the Area of the Circle

Finally, we can calculate the area of the circle using the formula mentioned earlier:

Area of the circle = (7 cm * 2.83 cm) / 2 ≈ 9.91 cm²

Therefore, the area of the circle inscribed in the triangle with side lengths 3 cm, 5 cm, and 6 cm is approximately 9.91 square centimeters.

Please note that the calculations provided are based on the given information and formulas.