Question

Допоможіть дуже срочно треба 1. Знайдіть площу круга, описаного навколо прямокутного трикутника із катетами 6 см і 8 см. 2. Знайдіть площу круга, вписаного у трикутник зі сторонами 30 см, 26 см і 8 см.​

Answer 1

Ответ:

Пошаговое объяснение:

s=$\frac{\pi }{4} *(a^{2}+b^{2} )$

78.5см2

2 см рисунок

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Answer 2

I can help you with your math problem.

1. To find the area of the circle circumscribed around a right triangle with legs 6 cm and 8 cm, we can use the formula:

$$S = \frac{\pi}{4}(a^2 + b^2)$$

where $a$ and $b$ are the lengths of the legs. This formula is derived from the fact that the hypotenuse of the right triangle is the diameter of the circle, and the radius is half of the hypotenuse. Therefore, the area of the circle is:

$$S = \frac{\pi}{4}(6^2 + 8^2) = \frac{\pi}{4}(36 + 64) = \frac{\pi}{4}(100) = 25\pi \approx 78.54 \text{ cm}^2$$

This answer is also given in the first web search result.

2. To find the area of the circle inscribed in a triangle with sides 30 cm, 26 cm and 8 cm, we can use the formula:

$$S = \frac{r}{2}(a + b + c)$$

where $r$ is the radius of the circle, and $a$, $b$ and $c$ are the lengths of the sides of the triangle. This formula is derived from the fact that the area of the triangle is equal to the sum of the areas of the three triangles formed by the radius and the sides. Therefore, the area of the circle is:

$$S = \frac{r}{2}(30 + 26 + 8) = 32r$$

To find the value of $r$, we can use Heron's formula to find the area of the triangle:

$$A = \sqrt{s(s - a)(s - b)(s - c)}$$

where $s$ is the semiperimeter of the triangle, given by:

$$s = \frac{a + b + c}{2} = \frac{30 + 26 + 8}{2} = 32$$

Therefore, the area of the triangle is:

$$A = \sqrt{32(32 - 30)(32 - 26)(32 - 8)} = \sqrt{32(2)(6)(24)} = \sqrt{9216} = 96 \text{ cm}^2$$

Since the area of the triangle is also equal to $32r$, we can solve for $r$:

$$32r = 96 \implies r = \frac{96}{32} = 3 \text{ cm}$$

Hence, the area of the circle is:

$$S = 32r = 32(3) = 96 \text{ cm}^2$$

This answer is also given in the third web search result.