Question

Сторона основания правильно треугольной призмы равна 6 см, а диагональ боковой грани равен 10 см. Найдите площадь боковой и полной поверхности призмы.

Answer 1

Сторона основания a= 6 см

Диагональ боковой грани d= 10 см

площадь основания So=a^2√3/4 =6^2√3/4=9√3 <- у призмы ДВА основания

высота призмы h=√d^2-a^2 =√ (10^2-6^2)=8 см

периметр P=3a =3*6=18 см

площадь боковой Sб=h*P=8*18=144 см2

площадь полной поверхности S=Sб+2*So=144+2*9√3=144+18√3 см2

ОТВЕТ 

144 см2

144+18√3 см2

Answer 2

Given Information:

We are given the following information about a right triangular prism: - The length of one side of the base is 6 cm. - The length of the diagonal of a lateral face is 10 cm.

Finding the Surface Area of the Lateral Face:

To find the surface area of the lateral face, we need to calculate the area of the right triangle formed by the side of the base and the diagonal of the lateral face.

Let's denote the base side length as a and the diagonal of the lateral face as d.

Using the Pythagorean theorem, we can find the height of the right triangle (which is also the height of the prism) as follows: h = sqrt(d^2 - a^2).

Substituting the given values, we have: h = sqrt(10^2 - 6^2) = sqrt(100 - 36) = sqrt(64) = 8 cm.

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Substituting the values, we have: Area = (1/2) * 6 cm * 8 cm = 24 cm^2.

Therefore, the surface area of the lateral face of the prism is 24 cm^2.

Finding the Total Surface Area of the Prism:

To find the total surface area of the prism, we need to consider the area of the two triangular bases in addition to the lateral face.

The area of a triangle is given by the formula: Area = (1/2) * base * height.

Substituting the values, we have: Area = (1/2) * 6 cm * 8 cm = 24 cm^2.

Since there are two triangular bases, the total area of the bases is 2 * 24 cm^2 = 48 cm^2.

The total surface area of the prism is the sum of the lateral face area and the base area: Total Surface Area = Lateral Face Area + 2 * Base Area.

Substituting the values, we have: Total Surface Area = 24 cm^2 + 48 cm^2 = 72 cm^2.

Therefore, the total surface area of the prism is 72 cm^2.

Summary:

- The surface area of the lateral face of the prism is 24 cm^2. - The total surface area of the prism is 72 cm^2.

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