Question

Дана правильная четырех угольная призма сторона основания 10 си боковая сторона 18 см найти полную поверхность призмы

Answer 1

S(полн)=S(бок)+2*S(осн)
S(бок)=10*18=180см²
S(осн)=10*10=100см²
S(полн)=180+2*100=380см²

Answer 2

Problem Analysis

We are given a right rectangular prism with the length of the base side equal to 10 cm and the lateral side equal to 18 cm. We need to find the total surface area of the prism.

Solution

To find the total surface area of a rectangular prism, we need to calculate the areas of all six faces and then sum them up.

The rectangular prism has two identical rectangular bases and four rectangular lateral faces.

Let's calculate the areas of each face:

1. Area of the base: The base is a rectangle with sides measuring 10 cm and 18 cm. The area of a rectangle is given by the formula length × width. Therefore, the area of the base is 10 cm × 18 cm = 180 cm².

2. Area of the top face: The top face is identical to the base, so its area is also 180 cm².

3. Area of the bottom face: The bottom face is identical to the base, so its area is also 180 cm².

4. Area of the front face: The front face is a rectangle with sides measuring 10 cm and 18 cm. Therefore, its area is also 10 cm × 18 cm = 180 cm².

5. Area of the back face: The back face is identical to the front face, so its area is also 180 cm².

6. Area of the side faces: There are two side faces, each with dimensions 10 cm (length) and 18 cm (height). Therefore, the area of each side face is 10 cm × 18 cm = 180 cm². Since there are two side faces, the total area of the side faces is 2 × 180 cm² = 360 cm².

Now, let's calculate the total surface area by summing up the areas of all the faces:

Total Surface Area = Area of the base + Area of the top face + Area of the bottom face + Area of the front face + Area of the back face + Total area of the side faces

Total Surface Area = 180 cm² + 180 cm² + 180 cm² + 180 cm² + 180 cm² + 360 cm²

Total Surface Area = 1,260 cm²

Therefore, the total surface area of the given prism is 1,260 cm².

Answer

The total surface area of the given prism is 1,260 cm².