Question

Высота правильной четырехугольной пирамиды 7 см , а сторона основания 8 см . Определить боковое ребро

Answer 1

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Answer 2

Calculation of the Slant Height of a Pyramid

To determine the slant height of a pyramid, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In the case of a pyramid, the slant height is the hypotenuse of a right triangle, with one of the other sides being the height of the pyramid and the other side being half the length of the base diagonal.

Let's calculate the slant height of the pyramid using the given information.

Given: - Height of the pyramid = 7 cm - Side length of the base = 8 cm

To find the slant height, we need to determine the length of the base diagonal. Since the base of the pyramid is a square, the diagonal of the base is equal to the side length multiplied by the square root of 2.

Let's calculate the base diagonal:

Base diagonal = Side length * √2 Base diagonal = 8 cm * √2

Using a calculator, we can find that the base diagonal is approximately 11.31 cm.

Now, we can use the Pythagorean theorem to find the slant height:

Slant height^2 = Height^2 + Base diagonal^2 Slant height^2 = 7 cm^2 + 11.31 cm^2

Using a calculator, we can find that the sum of the squares is approximately 170.96 cm^2.

Taking the square root of both sides, we find:

Slant height ≈ √170.96 cm Slant height ≈ 13.07 cm

Therefore, the slant height of the pyramid is approximately 13.07 cm.

Please note that the calculations are approximate due to rounding.

Conclusion

The slant height of the given pyramid, with a height of 7 cm and a side length of the base of 8 cm, is approximately 13.07 cm.