Question

ООООЧЕНЬ СРОЧНО ДАЮ 30 Балла Сторони трикутника трикутника дорівнюють 6 см, 6 см, 8 см. Знайдіть площу і радіус кола, вписаного у трикутник.​

Answer 1

Ответ:

r = $\sqrt{3,2}$ , S ≈ 10 см

Объяснение:

1) р = Р/2 = (6+6+8)/2 = 10 см

2) r = $\sqrt{((p-a)(p-b)(p-c))/p }$ = $\sqrt{((10-6)(10-6)(10-8))/10}$ =

$\sqrt{(4*4*2)/10}$ = $\sqrt{32/10}$ = $\sqrt{3,2}$

3) S = π$r^{2}$ = π*$3,2^{2}$ = 3,14*3,2 = 10,048 ≈ 10 cм

Answer 2

Triangle with Sides of 6 cm, 6 cm, and 8 cm

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

Area of the triangle = Semiperimeter * Inradius

where the semiperimeter is half the sum of the lengths of the triangle's sides, and the inradius is the radius of the inscribed circle.

In this case, the sides of the triangle are given as 6 cm, 6 cm, and 8 cm.

Calculating the Semiperimeter

The semiperimeter (s) of a triangle is calculated by adding the lengths of all three sides and dividing the sum by 2.

For the given triangle with sides of 6 cm, 6 cm, and 8 cm, the semiperimeter can be calculated as follows:

s = (6 cm + 6 cm + 8 cm) / 2 = 20 cm / 2 = 10 cm

Calculating the Inradius

The inradius (r) of a triangle can be calculated using the formula:

Inradius = Area of the triangle / Semiperimeter

To find the area of the triangle, we can use Heron's formula, which is given by:

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

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

Using the values we have, we can calculate the area of the triangle:

Area of the triangle = √(10 cm * (10 cm - 6 cm) * (10 cm - 6 cm) * (10 cm - 8 cm)) = √(10 cm * 4 cm * 4 cm * 2 cm) = √(320 cm^2) ≈ 17.89 cm^2

Now, we can calculate the inradius:

Inradius = Area of the triangle / Semiperimeter = 17.89 cm^2 / 10 cm ≈ 1.79 cm

Conclusion

The area of the triangle is approximately 17.89 cm^2 and the radius of the circle inscribed in the triangle is approximately 1.79 cm.