Question

В правильной четырехугольной призме сторона основания равна 4 см, диагональ призмы - 9 см. Найдите площадь боковой поверхности призмы.

Answer 1

Основание квадрат
диагональ основания 4√2 см
боковое ребро призмы √(9²-(4√2)²) = √(81-32) = √49 = 7 см
S=P*h= 4a*h = 4*4*7=112 см²

Answer 2

Calculation of the lateral surface area of a prism

To find the lateral surface area of a prism, we need to know the length of the base side and the length of the diagonal of the prism.

Given: - Length of the base side = 4 cm - Diagonal of the prism = 9 cm

To calculate the lateral surface area of the prism, we can use the formula:

Lateral Surface Area = Perimeter of the base x Height

In a rectangular prism, the perimeter of the base is equal to the sum of all the sides of the base. Since the base is a square, all sides are equal.

Let's calculate the perimeter of the base:

Perimeter of the base = 4 x Length of the base side

Substituting the given value, we have:

Perimeter of the base = 4 x 4 cm = 16 cm

Now, we need to find the height of the prism. The height can be calculated using the Pythagorean theorem, where the diagonal of the prism is the hypotenuse and the base side is one of the legs.

Let's calculate the height of the prism:

Height = √(Diagonal^2 - Base side^2)

Substituting the given values, we have:

Height = √(9 cm^2 - 4 cm^2) = √(81 cm^2 - 16 cm^2) = √65 cm ≈ 8.06 cm

Now that we have the perimeter of the base (16 cm) and the height (8.06 cm), we can calculate the lateral surface area:

Lateral Surface Area = Perimeter of the base x Height

Lateral Surface Area = 16 cm x 8.06 cm = 128.96 cm²

Therefore, the lateral surface area of the given prism is approximately 128.96 cm².