Question

Боковое ребро правильной треугольной призмы в 4 раза больше стороны основания, а сумма длин всех ребер равна 36.Найдите площадь полной поверхности призмы

Answer 1

36=6a+3*4a
a=36/18/2(см)
S(осн)=a^2 корней из 3 на 4=корень из 3(см2)
H=4a=8(см)
S(полн)=P(осн)*H+2S(осн)=2 корня из 3+3a*8=48+2 корня из 3(см2)
Ответ:48+2 корня из 3(см2)

Answer 2

Problem Analysis

We are given that the length of one of the lateral edges of a right triangular prism is 4 times the length of one side of the base, and the sum of the lengths of all the edges is 36. We need to find the total surface area of the prism.

Solution

Let's assume that the length of one side of the base of the prism is x.

Since the length of one of the lateral edges is 4 times the length of one side of the base, the length of the lateral edge can be expressed as 4x.

The sum of the lengths of all the edges of the prism is given as 36.

We can write the equation for the sum of the lengths of all the edges as:

x + x + x + 4x + 4x + 4x = 36

Simplifying the equation, we get:

14x = 36

Solving for x, we find:

x = 36 / 14

Now that we have the value of x, we can calculate the length of the lateral edge:

4x = 4 * (36 / 14)

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

The area of a triangle can be calculated using the formula: Area = (base * height) / 2.

The area of a rectangle can be calculated using the formula: Area = length * width.

Let's calculate the areas of the triangular bases and the rectangular lateral faces.

The area of one triangular base is:

Area of triangular base = (x * x) / 2

The area of the other triangular base is also the same.

The area of one rectangular lateral face is:

Area of rectangular lateral face = x * 4x

The area of the other two rectangular lateral faces is also the same.

Finally, we can calculate the total surface area of the prism by adding the areas of the two triangular bases and the three rectangular lateral faces.

Total surface area = 2 * (Area of triangular base) + 3 * (Area of rectangular lateral face)

Let's calculate the values and find the total surface area of the prism.