Question

чему равна площадь треугольника если периметр равен 12 см. а радиус вписаного круга 4 см

Answer 1

p=P/2=6

S=p*r=6*4=24

Answer 2

24 cm*2

potomushto p=6,r=4,S=6*4=24

Answer 3

Calculation of the Triangle's Area

To find the area of a triangle, we need to know the length of its sides or some other relevant information. In this case, we are given the perimeter of the triangle, which is 12 cm, and the radius of the inscribed circle, which is 4 cm.

Let's denote the sides of the triangle as a, b, and c, and the radius of the inscribed circle as r. The perimeter of the triangle is the sum of its sides:

a + b + c = 12 cm The radius of the inscribed circle can be related to the sides of the triangle using the formula:

r = (a + b - c) / 2 We can solve these equations simultaneously to find the lengths of the sides of the triangle.

Solving the Equations

Substituting the value of r from equation into equation we get:

(a + b - c) / 2 + c = 12 cm

Simplifying the equation, we have:

a + b - c + 2c = 24 cm

Combining like terms, we get:

a + b + c = 3c + 24 cm

Since we know that a + b + c = 12 cm, we can substitute this value into the equation:

12 cm = 3c + 24 cm

Simplifying the equation, we have:

3c = -12 cm

Dividing both sides by 3, we get:

c = -4 cm

However, the length of a side cannot be negative, so we discard this solution.

Finding the Lengths of the Other Sides

Since we couldn't find the length of side c, we need to approach the problem differently. Let's consider the formula for the area of a triangle:

Area = (1/2) * base * height

In an isosceles triangle, the height is also the perpendicular bisector of the base. Therefore, the height of the triangle is equal to the radius of the inscribed circle, which is 4 cm.

Let's denote the base of the triangle as b. We can divide the triangle into two right-angled triangles, each with a base of b/2 and a height of 4 cm. Using the Pythagorean theorem, we can find the lengths of the sides of these right-angled triangles.

Calculating the Length of the Base

Using the Pythagorean theorem, we have:

((b/2)^2) + (4^2) = (b^2)

Simplifying the equation, we get:

(b^2)/4 + 16 = b^2

Multiplying both sides by 4, we get:

b^2 + 64 = 4b^2

Rearranging the equation, we have:

3b^2 = 64

Dividing both sides by 3, we get:

b^2 = 64/3

Taking the square root of both sides, we get:

b = sqrt(64/3) cm

Calculating the Area of the Triangle

Now that we know the length of the base b, we can calculate the area of the triangle using the formula:

Area = (1/2) * base * height

Substituting the values, we have:

Area = (1/2) * sqrt(64/3) cm * 4 cm

Simplifying the equation, we get:

Area = 2 * sqrt(64/3) cm^2

Calculating the value, we find:

Area ≈ 8.77 cm^2

Therefore, the approximate area of the triangle is 8.77 cm^2.

Please note that the negative solution for side c was discarded because the length of a side cannot be negative.