Question

Основание пирамиды служить паралеллограм у которого стороны равны 3 и 6 , аодна из диагоналей 6 . Высота пирамиды проходит через точку пересечения диагоналей основания и равна 6 . Найдете боковое ребро пирамиды

Answer 1

Так как основание пирамиды — параллелограмм, то BO = DO и АО = ОС. Тогда треугольники AOS и COS равны по двум катетам. Треугольники BOS и DOS также равны. Так что BS = DS и AS = CS.
АС=6, т.е. АО= ОС=3
AS=CS= √3²+6²= √45=3√5
в параллелограмме сумма квадратов всех сторон равна сумме квадратов диагоналей, то есть
2 *AB² + 2*AD² = BD² +AC²
BD= √2*3²+2*6²- 6²= √54= 3√6 вторая диагональ, ВО=OD=3/2√6
по теореме Пифагора
BS=SD=√6²+ 3/2√6²= √36+ 9/4*6= √49.5

Answer 2

Finding the Side Length of the Pyramid

To find the side length of the pyramid, we can use the given information about the parallelogram base and the height of the pyramid.

Let's break down the given information: - The sides of the parallelogram base are equal to 3 and 6. - One of the diagonals of the parallelogram base is 6. - The height of the pyramid passes through the point of intersection of the diagonals of the base and is equal to 6.

To find the side length of the pyramid, we can use the Pythagorean theorem. The side length of the pyramid will be the hypotenuse of a right triangle formed by one side of the parallelogram base, half of the diagonal of the base, and the height of the pyramid.

Let's denote the side length of the pyramid as s.

Using the Pythagorean theorem, we can set up the following equation:

s^2 = (3/2)^2 + 6^2

Simplifying the equation:

s^2 = 9/4 + 36

s^2 = 45/4

Taking the square root of both sides:

s = √(45/4)

Simplifying further:

s = (3√5)/2

Therefore, the side length of the pyramid is (3√5)/2.

Please note that the above calculation assumes that the given information is accurate and that the pyramid is a regular pyramid with a parallelogram base.