The base of the pyramid is a rectangle, the sides of which are 16 roots 3 cm and 16 cm. The height of the pyramid

| March 11, 2021 | education

The base of the pyramid is a rectangle, the sides of which are 16 roots 3 cm and 16 cm. The height of the pyramid passes through the top of the base and is equal to 12 cm  Calculate the lengths of the side edges of the pyramid.

As you know from the school course, the height in such a pyramid will drop to the point of intersection of the diagonals of the rectangle.

Let us determine what the diagonal of a given rectangle will be if it is precisely known from the condition of our problem that the lengths of its side are 16√3 and 16 centimeters, respectively:

√ (16 ^ 2 + (16√3) ^ 2) = √ (162 * 4) = 32.

As we know, the diagonals will split in half when they intersect, so:

32: 2 = 16.

Now we find the side rib, knowing that the height is 12 cm:

√ (16 ^ 2 + 12 ^ 2) = 20.

Answer: 20 cm.



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