Question

в правильной треугольной пирамиде с объёмом равным 10 расстоянием между вершинами и точкой пересечения мередиан основания равна 5 найдите площадь основания пирамиды

Answer 1

Vпир = 1/3 * Sосн * h

V = 10, h = 5.

S = 6

Answer 2

Calculation of the Base Area of a Right Triangular Pyramid

To find the base area of a right triangular pyramid, we need to use the given information about the volume and the distance between the vertices and the intersection point of the medians of the base.

Let's break down the problem step by step:

1. We are given that the volume of the pyramid is 10. 2. We are also given that the distance between the vertices and the intersection point of the medians of the base is 5.

To find the base area, we can use the formula for the volume of a pyramid:

Volume of a pyramid = (1/3) * base area * height

In this case, the height is not given, but we can express it in terms of the volume and the base area:

Height = (3 * volume) / base area

Substituting the given volume (10) and the height expression into the formula, we get:

10 = (1/3) * base area * [(3 * volume) / base area]

Simplifying the equation, we have:

10 = (3 * volume) / base area

Now, we can solve for the base area:

**base area