Question

Сторона квадрата, описанного около окружности, равна 2 см. Чему равна площадь правильного треугольника, вписанного в эту окружность?

Answer 1

Ответ:

d = 2

стор. впис. тр =

$1 = \frac{a \sqrt{3} }{3}$

$a = \sqrt{3}$

S впис. тр. =

$\frac{3 \sqrt{3} }{4 \times 1}$

S =

$0.75 \sqrt{3}$

Answer 2

b квадрата = 2см    r окружности = 1/2 b = 1 см

S треугольника = $\alpha ^{2}$$\sqrt{3}$/4

R окружности = a/$\sqrt{3$

а= R*$\sqrt{3}$ = $\sqrt{3}$

S треугольника = 3$\sqrt{3$/4

Answer 3

Task: Find the area of a regular triangle inscribed in a circle with a side length of 2 cm.

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

Area of the triangle = (side length)^2 * sqrt(3) / 4

Given that the side length of the square circumscribed around the circle is 2 cm, we can use this value to calculate the area of the triangle.

Solution:

The side length of the square is equal to the diameter of the circle, which is twice the radius of the circle. Therefore, the radius of the circle is 1 cm.

Using the formula mentioned above, we can calculate the area of the triangle:

Area of the triangle = (2 cm)^2 * sqrt(3) / 4

Simplifying the equation:

Area of the triangle = 4 * sqrt(3) / 4 cm^2

The 4 in the numerator and denominator cancel out, leaving us with:

Area of the triangle = sqrt(3) cm^2

Therefore, the area of the regular triangle inscribed in the circle with a side length of 2 cm is sqrt(3) cm^2.

Please note that the answer provided is based on the information given and the mathematical formula for calculating the area of a regular triangle inscribed in a circle.