Question

Дно пирамиды представляет собой прямоугольник диагональю 12 см. Каждая сторона пирамиды составляет 10 см. Найдите высоту.

Answer 1

1.) 10*4=40
2.)40-12=32

Answer 2

Finding the Height of the Pyramid

To find the height of the pyramid, we can use the Pythagorean theorem. The diagonal of the base of the pyramid forms a right triangle with the height and one of the sides of the pyramid. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides.

Let's denote the height of the pyramid as h and the side length of the pyramid as s.

Using the Pythagorean theorem, we have:

s^2 = (s/2)^2 + h^2

Simplifying the equation, we get:

s^2 = (s^2)/4 + h^2

Multiplying both sides of the equation by 4, we get:

4s^2 = s^2 + 4h^2

Rearranging the equation, we have:

3s^2 = 4h^2

Taking the square root of both sides, we get:

sqrt(3s^2) = 2h

Simplifying further, we have:

sqrt(3)s = 2h

Finally, we can solve for the height h:

h = (sqrt(3)s)/2

Now, let's substitute the given values into the equation to find the height of the pyramid.

The diagonal of the base is given as 12 cm, so s = 12 cm.

Substituting this value into the equation, we have:

h = (sqrt(3) * 12) / 2

Calculating the value, we find:

h ≈ 10.392 cm

Therefore, the height of the pyramid is approximately 10.392 cm.