Question

В правильной ,четырёхугольной пирамиде боковое ребро 7 см и апофема 4 см . найдите ребро основания пирамиды

Answer 1

Пирамида правильная, в основании лежит квадрат, значит грани представляют равнобедренные треугольники, апофема высота одной из этих граней, а значит и медиана. По теореме Пифагора найдём половину стороны основания: $\sqrt{7^{2} -4^{2} } = \sqrt{49-16}= \sqrt{33}$, значит ребро основания пирамиды равно $2 \sqrt{33}$.

Answer 2

Finding the Base Edge of a Quadrilateral Pyramid

To find the base edge of a quadrilateral pyramid, we can use the given information of the lateral edge and the apothem.

Let's denote the base edge of the pyramid as x.

According to the given information: - The lateral edge of the pyramid is 7 cm. - The apothem (distance from the center of the base to the midpoint of any side) is 4 cm.

To find the base edge, we can use the formula for the slant height of a pyramid, which relates the lateral edge, apothem, and base edge:

Slant Height (s) = √(lateral edge^2 - apothem^2)

In this case, the slant height is equal to the lateral edge, so we can rewrite the formula as:

7 cm = √(x^2 - 4^2)

To solve for x, we can square both sides of the equation:

49 cm^2 = x^2 - 16 cm^2

Adding 16 cm^2 to both sides:

65 cm^2 = x^2

Taking the square root of both sides:

x = √65 cm

Therefore, the base edge of the pyramid is approximately 8.06 cm.

Please note that the above calculations are based on the given information and assumptions about the shape of the pyramid.