Question

Найтиплощадь круга,вкоторый вписантреугольниксо сторонами6,8,10 с розвязкой

Answer 1

Площадь круга: S=ПиR²
Значит
R=(a*b*c)/4S
Найдем площать треугольника: S=√p(p-a)(p-b)(p-c)
Где P=(a+b+c)/2
Найдем р:
(6+8+10)/2=24/2=12
Тепреь найдём S:
√12(12-6)(12-8)(12-10)=√12*6*4*2=√144=12см²
Теперь, зная площадь треугольника, найдем R:
R=(6*8*10)/4*12
R=480/48
R=10 см

А формула площади круга такова: S=ПиR²
S=3.14*100
S=314 cм²
Вооот:)

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 its three sides - r is the radius of the inscribed circle

In this case, the triangle has sides of length 6, 8, and 10. Let's calculate the semi-perimeter first:

Semi-perimeter (s) = (6 + 8 + 10) / 2 = 12

Now, we need to find the radius of the inscribed circle. We can use the formula:

Radius (r) = Area of the triangle / Semi-perimeter (s)

To find the area of the triangle, we can use Heron's formula:

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

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

Let's calculate the area of the triangle first:

Area of the triangle = √(12 * (12 - 6) * (12 - 8) * (12 - 10)) = √(12 * 6 * 4 * 2) = √(576) = 24

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

Radius (r) = 24 / 12 = 2

Finally, we can find the area of the circle:

Area of the circle = (12 * 2) / 2 = 12

Therefore, the area of the circle inscribed in the triangle with sides 6, 8, and 10 is 12 square units.

Answer

The area of the circle inscribed in the triangle with sides 6, 8, and 10 is 12 square units.