Question

Высота правельной четырёх угольноц пирамиды равна 5см а сторона основания 6см найти боковое ребро

Answer 1

Сначала нужно найти диагональ основания
$d=\sqrt{2\cdot6^2}=\sqrt{72}$
Рассмотрим прямоугольный треугольник, образованный высотой пирамиды, её ребром и половиной диагонали основания. С помощью теоремы Пифагора найдём ребро 
$r=\sqrt{5^2+(\frac{\sqrt{72}}{2})^2}=\sqrt{43}$

Answer 2

Problem Analysis

We are given the height and the side length of a regular quadrilateral pyramid and we need to find the length of the lateral edge.

Solution

To find the length of the lateral edge, we can use the formula for the slant height of a regular quadrilateral pyramid. The slant height can be calculated using the height and the side length of the pyramid.

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

The slant height (l) can be calculated using the formula:

l = sqrt(h^2 + (a/2)^2)

Substituting the given values, we have:

h = 5 cm (given) a = 6 cm (given)

Substituting these values into the formula, we get:

l = sqrt(5^2 + (6/2)^2) = sqrt(25 + 9) = sqrt(34) cm

Therefore, the length of the lateral edge of the pyramid is sqrt(34) cm.

Answer

The length of the lateral edge of the regular quadrilateral pyramid is sqrt(34) cm.

Explanation

A regular quadrilateral pyramid is a pyramid with a quadrilateral base and all its faces are congruent isosceles triangles. The lateral edge is the edge connecting the apex of the pyramid to a point on the base that is not a vertex.

To find the length of the lateral edge, we can use the formula for the slant height of a regular quadrilateral pyramid. The slant height is the distance from the apex to a point on the base along the lateral edge.

In this case, we are given the height of the pyramid as 5 cm and the side length of the base as 6 cm. Using the formula for the slant height, we can calculate the length of the lateral edge as sqrt(34) cm.

Additional Information

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