В правильной треугольной пирамиде полная поверхность рае
См2, а площадь основания - 4 V3 см2. Найдите апофему и плос.. при вершине пирамиды.
To find the apothem and slant height of a right triangular pyramid, we need to use the formula a = (b^2 + h^2)^(1/2) for the apothem and s = (a^2 + h^2)^(1/2) for the slant height. Let's plug in the given values: a = ((4√3)^2 + h^2)^(1/2) = (16/3 + h^2)^(1/2). Since we don't have information about the height, we cannot find the exact values of a and s. However, we can express them in terms of h. Let's take a look at the triangle with one of its legs as the apothem and the other leg as half of the base. According to Pythagorean theorem, we have (h/2)^2 + a^2 = (4√3/2)^2. Plugging in the values of a and simplifying, we get: h^2 + (16/3 + h^2)^(1/2) = 4*3/2^2 = 6. Rearranging the equation, we get h^2 + (16/3 + h^2) = 36. Simplifying, we get h^2 + 16/3 = 36. Multiplying both sides by 3, we get 3h^2 + 16 = 108. Subtracting 16 from both sides, we get 3h^2 = 92. Dividing both sides by 3, we get h^2 = 92/3. Taking the square root, we get h = (92/3)^1/2 = (4*23/3)^1/2 = (4 + 23)^(1/2) = 7. Now we can find the values of a and s using the formulas. Let's start with a: a = (16/3 + h^2)^(1/2) = (16/3 + 49)^(1/2) = (12 + 49)^(1/2) = 61^(1/2) = √61. And for s: s = (a^2 + h^2)^(1/2) = (61 + 49)^(1/2) = 110^(1/2) = √110. Therefore, the apothem and slant height of the pyramid are approximately √61 cm and √110 cm, respectively.
