Question

Сторона основания правильной четырехугольной призмы равна 5см,а высота 9см.Вычислите площадь боковой и полной поверхности призмы

Answer 1

Площадь боковой поверхности= 5*9*4=180 Площадь полной вредности призмы= боковая+ основание=180+5*5=205

Answer 2

Calculation of the lateral surface area and total surface area of a prism

To calculate the lateral surface area and total surface area of a prism, we need to know the length of the base and the height of the prism.

Given: - Length of the base = 5 cm - Height of the prism = 9 cm

Lateral Surface Area of the Prism

The lateral surface area of a prism is the sum of the areas of all the lateral faces. In the case of a rectangular prism, the lateral faces are all rectangles.

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

Lateral Surface Area = Perimeter of the base x Height

Since the base of the prism is a rectangle, the perimeter of the base is equal to the sum of all the sides of the rectangle.

In this case, the base of the prism is a square with a side length of 5 cm. Therefore, the perimeter of the base is 4 times the length of one side.

Perimeter of the base = 4 x 5 cm = 20 cm

Now we can calculate the lateral surface area:

Lateral Surface Area = 20 cm x 9 cm = 180 cm².

Therefore, the lateral surface area of the prism is 180 cm².

Total Surface Area of the Prism

The total surface area of a prism is the sum of the areas of all the faces, including the bases and the lateral faces.

To calculate the total surface area of a rectangular prism, we use the formula:

Total Surface Area = 2 x Base Area + Lateral Surface Area

The base area of a rectangular prism is equal to the area of the base, which is a square with a side length of 5 cm.

Base Area = 5 cm x 5 cm = 25 cm²

Now we can calculate the total surface area:

Total Surface Area = 2 x 25 cm² + 180 cm² = 50 cm² + 180 cm² = 230 cm².

Therefore, the total surface area of the prism is 230 cm².

In summary: - The lateral surface area of the prism is 180 cm². - The total surface area of the prism is 230 cm².

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