Question

У правильной четырехугольной призмы сторона основания равна 4 см а боковое ребро 5 см Найти площадь полной поверхности ЗАРАНЕЕ БЛАГОДАРСТВУЮ даю 20 баллов на сегодня

Answer 1

Площадь полной поверхности призмы: S=2(ab+bc+ac).
Так как a=b, то S=2(a²+2ac)=2a(a+2c)=2·4(4+2·5)=112 см² - это ответ. 

Answer 2

Calculation of the Total Surface Area of a Prism

To find the total surface area of a prism, we need to calculate the areas of all its faces and then sum them up. In the case of a rectangular prism, the total surface area can be found using the formula:

Total Surface Area = 2 * (Area of Base) + (Perimeter of Base) * (Height)

In this case, the rectangular prism has a base with a side length of 4 cm and a lateral edge (height) of 5 cm. Let's calculate the total surface area step by step.

Step 1: Calculate the Area of the Base

Since the base of the prism is a rectangle, the area of the base can be calculated using the formula:

Area of Base = Length * Width

In this case, the length and width of the base are both 4 cm. Therefore, the area of the base is:

Area of Base = 4 cm * 4 cm = 16 cm².

Step 2: Calculate the Perimeter of the Base

The perimeter of the base can be calculated by adding up the lengths of all four sides of the rectangle. Since the length and width of the base are both 4 cm, the perimeter of the base is:

Perimeter of Base = 2 * (Length + Width) = 2 * (4 cm + 4 cm) = 2 * 8 cm = 16 cm.

Step 3: Calculate the Total Surface Area

Now that we have the area of the base and the perimeter of the base, we can calculate the total surface area using the formula mentioned earlier:

Total Surface Area = 2 * (Area of Base) + (Perimeter of Base) * (Height).

Substituting the values we calculated earlier:

Total Surface Area = 2 * (16 cm²) + (16 cm) * (5 cm) = 32 cm² + 80 cm² = 112 cm².

Therefore, the total surface area of the given rectangular prism is 112 cm².

I hope this helps! Let me know if you have any further questions.