Question

В основі піраміди лежить паралелограм зі сторонами 21 см і 9 см,а одна з його діагоналей 18см. Знайти бічні ребра піраміди,якщо висота піраміди ,яка проходить через точку перетину діагоналей, дорівнює 12см

Answer 1

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Answer 2

Finding the lateral edges of the pyramid

To find the lateral edges of the pyramid, we need to determine the lengths of the sides of the parallelogram base. We are given that the sides of the parallelogram are 21 cm and 9 cm, and one of its diagonals is 18 cm. We also know that the height of the pyramid passing through the intersection point of the diagonals is 12 cm.

Let's start by finding the length of the other diagonal of the parallelogram. We can use the properties of a parallelogram to determine this length. In a parallelogram, the diagonals bisect each other, so each half of the diagonal is equal to the height of the parallelogram.

The height of the parallelogram is given as 12 cm, so each half of the diagonal is 12 cm. Therefore, the length of the other diagonal is 2 times 12 cm, which is 24 cm.

Now, we can use the lengths of the sides and diagonals of the parallelogram to find the lateral edges of the pyramid. The lateral edges are the slant heights of the triangular faces that make up the pyramid.

Using the Pythagorean theorem, we can find the length of the lateral edges. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the lateral edge is the hypotenuse, and the sides of the right triangle are half of the diagonal (12 cm) and one of the sides of the parallelogram (9 cm).

Let's calculate the length of the lateral edge using the Pythagorean theorem:

Step 1: Square the lengths of the sides and add them together: (12 cm)^2 + (9 cm)^2 = 144 cm^2 + 81 cm^2 = 225 cm^2

Step 2: Take the square root of the sum: √(225 cm^2) = 15 cm

Therefore, the length of each lateral edge of the pyramid is 15 cm.