Question

СРОЧНО НУЖНО ПОЖАЛУЙСТА • Дано трикутник АВС. Точка А1 лежить на продовженні сторони ВС за точку С, причому ВС=СА1, точка В1, лежить на продовженні сторони СА за точку A і B1A=АС, а точка С1 лежить на продовженні сторони АВ за точку В і ВС1=AB. Знайти плошщу трикутника A1B1C1, якщо площа трикутника АВС=1.

Answer 1

Ответ:

Объяснение:

∆АВС, является ∆ , построенным на средних линиях ∆А1В1С1,

И его S в 4 раза больше S(ABC)

см. Картинку

Answer 2

To find the area of triangle A1B1C1, we need to use the given information and apply some geometric principles. Let's break down the problem step by step.

Given Information:

- Triangle ABC is given. - Point A1 lies on the extension of side BC beyond point C, and BC = CA1. - Point B1 lies on the extension of side CA beyond point A, and B1A = AC. - Point C1 lies on the extension of side AB beyond point B, and BC1 = AB. - The area of triangle ABC is 1.

Approach:

To find the area of triangle A1B1C1, we can use the concept of similar triangles. Since the sides of triangle ABC and triangle A1B1C1 are proportional, we can find the ratio of their areas.

Solution:

Let's denote the area of triangle A1B1C1 as x.

Since triangle ABC and triangle A1B1C1 are similar, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

The ratio of side lengths BC to A1B1 is 1:1, so the ratio of their areas is (1:1)^2 = 1:1.

Similarly, the ratio of side lengths AC to B1C1 is 1:1, so the ratio of their areas is (1:1)^2 = 1:1.

Finally, the ratio of side lengths AB to C1A1 is 1:1, so the ratio of their areas is (1:1)^2 = 1:1.

Since the area of triangle ABC is 1, the area of triangle A1B1C1 is also 1.

Answer:

The area of triangle A1B1C1 is 1.

Please let me know if you need any further clarification or assistance!