Question

У прямокутному паралепіпеді сторони основи 6 і 8 утв. кут 30 градусів бічне ребро = 5 метрів знайдіть повну поверхню площи паралепіпеда.

Answer 1

Sпол.=2Sосн.+Sбок.=2*6*8*sin30°+2*(6+8)*5=48+140=188(м²)

Answer 2

Calculating the Total Surface Area of a Rectangular Parallelepiped

To calculate the total surface area of a rectangular parallelepiped, we can use the formula:

Total Surface Area = 2lw + 2lh + 2wh

Where: - l = length of the parallelepiped - w = width of the parallelepiped - h = height of the parallelepiped

Let's calculate the total surface area using the given dimensions and angle.

Given Dimensions and Angle

- Length of the base (l) = 8 - Width of the base (w) = 6 - Angle between the base and the lateral edge = 30 degrees - Length of the lateral edge = 5

Calculating the Height of the Parallelepiped

To calculate the height of the parallelepiped, we can use the formula: Height = lateral edge * sin(angle)

Substituting the given values: Height = 5 * sin(30°)

Let's calculate the height.

Calculations

Using the given values: Height = 5 * sin(30°) Height ≈ 5 * 0.5 Height = 2.5

Now that we have the height, we can calculate the total surface area using the formula mentioned earlier.

Total Surface Area Calculation

Substituting the given values: Total Surface Area = 2lw + 2lh + 2wh Total Surface Area = 2(6*8) + 2(6*2.5) + 2(8*2.5) Total Surface Area = 96 + 30 + 40 Total Surface Area = 166 square units

So, the total surface area of the rectangular parallelepiped is approximately 166 square units.