Question

Найдите площадь полной поверхности прямой призмы, в основании которой ромб с диагоналями 12 и 16 см. Высота призмы 10 см. Желательно с рисунком.

Answer 1

Ответ:

592 см²

Объяснение:

Найдите площадь полной поверхности прямой призмы, в основании которой ромб с диагоналями 12 и 16 см. Высота призмы 10 см. Желательно с рисунком

Answer 2

Calculation of the Surface Area of a Prism

To find the 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 right prism with a rhombus as its base, we can break it down into three parts: the top and bottom faces (which are congruent rhombi) and the four side faces (which are rectangles).

Let's calculate the surface area step by step:

1. Calculate the area of the rhombus base: - The diagonals of the rhombus are given as 12 cm and 16 cm. - The formula to calculate the area of a rhombus is (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals. - Substituting the given values, we get (12 cm * 16 cm) / 2 = 96 cm².

2. Calculate the area of each rectangle side face: - The height of the prism is given as 10 cm. - The length of each side face is equal to the length of the corresponding side of the rhombus base. - The formula to calculate the area of a rectangle is length * height. - Substituting the given values, we get 4 * (12 cm * 10 cm) = 480 cm².

3. Calculate the total surface area: - The total surface area of the prism is the sum of the areas of the base and the side faces. - Adding the area of the base (96 cm²) to the area of the side faces (480 cm²), we get a total surface area of 576 cm².

Therefore, the total surface area of the given prism is 576 cm².

Diagram:

Here is a diagram to help visualize the prism:

       A
      / \
     /   \
    /     \
   /       \
  B---------C
   \       /
    \     /
     \   /
      \ /
       D

In the diagram, A, B, C, and D represent the vertices of the rhombus base, and the lines connecting them represent the sides of the rhombus. The height of the prism is represented by vertical lines extending from each vertex of the base.

Please note that the diagram is not to scale and is only meant to provide a visual representation of the prism.