Question

В правильной треугольной призме сторона основания равна 4 см, высота призмы равна 10 см. Вычислите плошадь полной поверхности призмы

Answer 1

В правильной треугольной призме сторона основания равна 4 см, высота призмы равна 10 см. Вычислите плошадь полной поверхности призмы

S=10·(3·4)+2·4·4·sin60°/2=120+(8√3)/2=120+4√3

Answer 2

Calculation of the Surface Area of a Right Triangular Prism

To calculate the surface area of a right triangular prism, we need to find the areas of the three rectangular faces and the two triangular faces.

Given: - Base side length = 4 cm - Prism height = 10 cm

Calculation Steps:

1. Calculate the area of the triangular face: - The triangular face is a right triangle with base and height equal to the base side length of the prism. - The area of a triangle is given by the formula: Area = (base * height) / 2. - Substituting the values, we get: Area of triangular face = (4 cm * 4 cm) / 2 = 8 cm².

2. Calculate the areas of the rectangular faces: - The rectangular faces are adjacent to the triangular face and have dimensions equal to the base side length and the prism height. - The area of a rectangle is given by the formula: Area = length * width. - Substituting the values, we get: Area of rectangular faces = 4 cm * 10 cm = 40 cm².

3. Calculate the total surface area: - The total surface area of the prism is the sum of the areas of all the faces. - Since there are two triangular faces and three rectangular faces, the total surface area is: Total surface area = 2 * Area of triangular face + 3 * Area of rectangular faces. - Substituting the values, we get: Total surface area = 2 * 8 cm² + 3 * 40 cm² = 16 cm² + 120 cm² = 136 cm².

Therefore, the total surface area of the right triangular prism is 136 cm².