Question

В правильный четырхугольной призме площадь основания равна 144 см2,а высота -14см.найдите диагональ призмы .

Answer 1

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Answer 2

Finding the Diagonal of a Prism

To find the diagonal of a rectangular prism, we can use the formula:

Diagonal = √(Length^2 + Width^2 + Height^2)

In this case, we are given that the area of the base of the prism is 144 cm² and the height is 14 cm. However, we don't have the length and width of the base. Therefore, we need to find the length and width before we can calculate the diagonal.

Finding the Length and Width of the Base

Since the prism is a rectangular prism, we can assume that the base is a rectangle. The area of the base is given as 144 cm². To find the length and width, we need to find two numbers that multiply to give 144 and have a difference of 0.

Let's find the factors of 144:

- 1 × 144 = 144 - 2 × 72 = 144 - 3 × 48 = 144 - 4 × 36 = 144 - 6 × 24 = 144 - 8 × 18 = 144 - 9 × 16 = 144 - 12 × 12 = 144

From these factors, we can see that the length and width of the base could be 12 cm and 12 cm, respectively.

Calculating the Diagonal

Now that we have the length (12 cm), width (12 cm), and height (14 cm) of the prism, we can calculate the diagonal using the formula mentioned earlier:

Diagonal = √(Length^2 + Width^2 + Height^2)

Substituting the values:

Diagonal = √(12^2 + 12^2 + 14^2)

Diagonal = √(144 + 144 + 196)

Diagonal = √(484)

Diagonal = 22 cm

Therefore, the diagonal of the given prism is 22 cm.