Question

Боковая поверхность правильной четырехугольной призмы равна 32кв.см, а полная поверхность - 40кв.см.Найдите высоту призмы. Ответ - 4м, решить не получается, заранее спасибо)))

Answer 1

S полная = 2 * Sоснований + 4 * Sбоковые

2 * Sоснований, т.к. верхнее основание и нижнее основание, а они равны.

4 * Sбоковые, т.4 у правильной четырехугольной призмы 4 боковые поверхности и они тоже равны.

2* Sоснований = 40 - 32 = 8 кв. см.

Sоснования= 4 кв.см, в основании лежит квадрат значит его сторона а = 2 см

4 * Sбоковые = 32

Sбоковая = 8

Sбоковая = а * h, отсюда h = Sбок : а = 8 : 2 = 4

Ответ. h = 4 см 

 

 

Answer 2

Calculation of the Height of the Prism

To find the height of the prism, we can use the given information about the lateral surface area and the total surface area of the prism.

Let's denote the lateral surface area as A and the total surface area as B.

Given: - Lateral surface area (A) = 32 cm² - Total surface area (B) = 40 cm²

The lateral surface area of a prism is calculated by multiplying the perimeter of the base by the height of the prism. The total surface area is calculated by adding the lateral surface area to twice the area of the base.

We can set up the following equations based on the given information:

Equation 1: A = perimeter of the base × height Equation 2: B = A + 2 × area of the base

To solve for the height, we need to find the perimeter of the base and the area of the base.

Since the prism is described as a "regular quadrilateral prism," we can assume that the base is a square.

Let's denote the side length of the base as s.

The perimeter of the base is given by 4s, and the area of the base is given by s².

Substituting these values into Equation 1 and Equation 2, we get:

Equation 1: 32 = 4s × height Equation 2: 40 = 32 + 2s²

Simplifying Equation 2, we have:

40 = 32 + 2s² 8 = 2s² 4 = s² s = 2 cm

Now, substituting the value of s into Equation 1, we can solve for the height:

32 = 4 × 2 × height 32 = 8 × height height = 32 / 8 height = 4 cm

Therefore, the height of the prism is 4 cm.

Please note that the answer provided is based on the given information and assumptions made about the shape of the base.