Question

в основании прямой призмы лежит прямоугольный треугольник с катетами 3см и 4см.Высота призмы равна 2см.Найдите площадь полной поверхности призмысрочно помогите(((

Answer 1

Sпол=2S осн+S бок

 S осн=1/2*3*4=6 см^2

площадь боковой поверхности состоит из трех прямоугольников

S 1-го прям-ка=2*3=6

 

 

 

  S 2-го прям-ка=2*4=8

 

 

 

 

  S 3-го прям-ка=2*5=10(третью сторону прямоульника нашли из прям. треуг-ка по теореме пифагора)

 Sпол=2*6+6+8+10 =36

 

 

 

 

Answer 2

I will answer in detail. The base of the right prism is a right triangle with legs 3 cm and 4 cm. The height of the prism is 2 cm. Find the area of the total surface of the prism.

Possible response:

To find the area of the total surface of the prism, we need to find the areas of the base, the top, and the three lateral faces. The base and the top are congruent right triangles with legs 3 cm and 4 cm, so their area is half the product of the legs: $$\frac{1}{2} \times 3 \times 4 = 6$$ cm$^2$. The three lateral faces are rectangles with one side equal to the height of the prism (2 cm) and the other side equal to the length of the corresponding side of the base. The lengths of the sides of the base are 3 cm, 4 cm, and 5 cm, where 5 cm is the hypotenuse of the right triangle. Therefore, the areas of the lateral faces are $$2 \times 3 = 6$$ cm$^2$, $$2 \times 4 = 8$$ cm$^2$, and $$2 \times 5 = 10$$ cm$^2$. The area of the total surface of the prism is the sum of the areas of all the faces: $$6 + 6 + 6 + 8 + 10 = 36$$ cm$^2$. You can see a diagram of the prism and its faces [here](https://nsportal.ru/shkola/geometriya/library/2021/03/03/ploshchad-poverhnosti-prizmy-reshenie-zadach), on slide 9. I hope this helps.