Question

Стороны основанием правильный четырехугольник пирамида равна 6 , боковое ребро равно 5 . Найти полную площадь

Answer 1

В пирамиде правильной ЕАВСД ЕА=5, АВ=6.
S=?

Площадь основания So=АВ²=36.

В равнобедренном треугольнике ЕАВ ЕМ - апофема, значит АМ=ВМ.
АМ=АВ/2=3.
В прямоугольном тр-ке ЕАМ отношение гипотенузы ЕА и катета АМ 5:3 - как в египетском треугольнике, значит ЕМ=4.
Площадь боковой поверхности Sб=P·l/2=4АВ·ЕМ/2,
Sб=4·6·4/2=48.

S=So+Sб=36+48=84 - это ответ.

Answer 2

Given Information

We are given that the base of a pyramid, which is a quadrilateral, has an area of 6 and one of the lateral edges has a length of 5.

Finding the Total Surface Area

To find the total surface area of the pyramid, we need to calculate the sum of the areas of all its faces.

Solution

Let's break down the solution into steps:

1. Find the area of the base: - We are given that the area of the base is 6. - Area of the base = 6.

2. Find the area of each triangular face: - Since the pyramid is a quadrilateral, it can be divided into four triangular faces. - To find the area of each triangular face, we need to calculate the length of the height of the pyramid. - Using the Pythagorean theorem, we can find the height of the pyramid by considering the lateral edge, the height of the triangular face, and half of the base diagonal. - The base diagonal can be found using the formula: base diagonal = 2 * base area / base length. - Substituting the given values, we have: base diagonal = 2 * 6 / 5 = 12 / 5. - Using the Pythagorean theorem, we can find the height of the pyramid: height = sqrt(lateral edge^2 - (base diagonal / 2)^2). - Substituting the given values, we have: height = sqrt(5^2 - (12 / 5 / 2)^2) = sqrt(25 - (6 / 5)^2) = sqrt(25 - 36 / 25) = sqrt(625 - 36) / 5 = sqrt(589) / 5. - Now, we can find the area of each triangular face using the formula: area of a triangle = 0.5 * base length * height. - Substituting the given values, we have: area of each triangular face = 0.5 * 5 * (sqrt(589) / 5) = sqrt(589) / 2. - Since there are four triangular faces, the total area of the triangular faces is: total area of triangular faces = 4 * (sqrt(589) / 2) = 2 * sqrt(589).

3. Find the total surface area: - The total surface area of the pyramid is the sum of the area of the base and the total area of the triangular faces. - Substituting the calculated values, we have: total surface area = area of the base + total area of triangular faces = 6 + 2 * sqrt(589).

Answer

The total surface area of the pyramid is 6 + 2 * sqrt(589).

Note: The answer is an exact value and cannot be simplified further.