Question

В правильной треугольной пирамиде SABC медианы основания пересекаются в точке О. Объём пирамиды равен 28, OS = 12. Найдите площадь треугольника АВС. Заранее огромное спасибо)

Answer 1

С формулы V=1/3Sосновы*Н получаем што  Sосновы = 3V/Н имеем (28*3)/12=7см^2

Если (АВС- основание пирамиды) ели нет напишы решу дальше

Answer 2

Given Information:

We are given a right triangular pyramid SABC, where the medians of the base intersect at point O. The volume of the pyramid is 28 and OS = 12. We need to find the area of triangle ABC.

Approach:

To find the area of triangle ABC, we can use the formula for the volume of a pyramid and the relationship between the medians and the sides of a triangle.

Solution:

1. Let's denote the lengths of the medians of triangle ABC as MA, MB, and MC. The medians of a triangle divide each other in the ratio 2:1. Therefore, we can write: - MA:MB:MC = 2:1:1

2. The volume of a pyramid can be calculated using the formula: - Volume = (1/3) * base area * height

3. In our case, the volume of the pyramid is given as 28. Let's denote the height of the pyramid as h and the area of triangle ABC as S. We can write: - 28 = (1/3) * S * h

4. We are also given that OS = 12. Since O is the centroid of triangle ABC, the medians divide each other in the ratio 2:1. Therefore, we can write: - OA:OS = 2:1

5. Using the given information, we can find the length of OA: - OA = (2/3) * OS = (2/3) * 12 = 8

6. Now, let's find the length of MA. Since O is the centroid, we can write: - OA:MA = 2:1 - MA = (3/2) * OA = (3/2) * 8 = 12

7. Similarly, we can find the lengths of MB and MC: - MB = (3/2) * OA = (3/2) * 8 = 12 - MC = (3/2) * OA = (3/2) * 8 = 12

8. Now, we can find the area of triangle ABC using the lengths of the medians: - S = (4/3) * √(s * (s - MA) * (s - MB) * (s - MC)), where s is the semi-perimeter of triangle ABC - s = (MA + MB + MC) / 2 = (12 + 12 + 12) / 2 = 18 - S = (4/3) * √(18 * (18 - 12) * (18 - 12) * (18 - 12)) - S = (4/3) * √(18 * 6 * 6 * 6) - S = (4/3) * √(6^4) - S = (4/3) * 6^2 - S = (4/3) * 36 - S = 48

Answer:

The area of triangle ABC is 48.