Question

В основании правильной пирамиды лежит пятиугольник. Найдите апофему пирамиды, если площадь боковой поверхности пирамиды равна 92,5, а сторона основания равна 5.

Answer 1

Апофема пирамиды - высота боковой грани.
Площадь одной грани равняется 1/5 от площади боковой поверхности=18,5
Т.к. пирамида правильная, треугольник равнобедренный, а апофема является и биссектрисой,  и высотой.
Апофема = 2s/a=  37/5 = 7,4.

Answer 2

Finding the Apothem of a Pyramid with a Pentagonal Base

To find the apothem of a pyramid with a pentagonal base, we need to use the given information: the lateral surface area of the pyramid is 92.5 and the side length of the base is 5.

The lateral surface area of a pyramid can be calculated using the formula:

Lateral Surface Area = (Perimeter of Base) × (Apothem) / 2

Since the base of the pyramid is a pentagon, we need to find the perimeter of the pentagon. The perimeter of a regular pentagon can be calculated using the formula:

Perimeter of a Regular Pentagon = 5 × (Side Length)

In this case, the side length of the pentagon is given as 5, so the perimeter of the pentagon is:

Perimeter of Pentagon = 5 × 5 = 25

Now, we can substitute the values into the formula for the lateral surface area:

92.5 = 25 × (Apothem) / 2

To find the apothem, we can rearrange the equation:

Apothem = (2 × 92.5) / 25

Simplifying the equation:

Apothem = 3.7

Therefore, the apothem of the pyramid is 3.7.