Question

Помогите решить, пожалуйста! В основании прямой призмы параллелограмм со сторонами 5 см и 8 см и углом между ними 30 градусов. Найти площадь полной поверхности призмы, если её боковое ребро равно 9 см.

Answer 1

Sполн = Sбок + 2Sосн =
= Pосн ·h + 2·(1/2 · a·b·sinα) = 2(5 + 8)·9 + 5·8·1/2 = 234 + 20 = 254

Answer 2

Problem Analysis

We are given a right prism with a parallelogram as its base. The sides of the parallelogram are 5 cm and 8 cm, and the angle between them is 30 degrees. The length of the lateral edge of the prism is 9 cm. We need to find the total surface area of the prism.

Solution

To find the total surface area of the prism, we need to calculate the areas of the base and the lateral faces.

Calculating the Base Area

The base of the prism is a parallelogram. The area of a parallelogram can be calculated by multiplying the length of the base by the height. In this case, the base has sides of 5 cm and 8 cm, and the angle between them is 30 degrees. To find the height, we can use the formula: height = side * sin(angle).

Let's calculate the base area:

Base Area = base length * height

Base Area = 5 cm * (8 cm * sin(30 degrees))

To calculate the sine of 30 degrees, we can use a calculator or refer to a trigonometric table. The sine of 30 degrees is 0.5.

Base Area = 5 cm * (8 cm * 0.5) = 20 cm^2 .

Calculating the Lateral Surface Area

The lateral surface area of a prism can be calculated by multiplying the perimeter of the base by the height of the prism. In this case, the perimeter of the base is the sum of the lengths of the sides of the parallelogram, which is 2 * (5 cm + 8 cm) = 26 cm. The height of the prism is given as 9 cm.

Lateral Surface Area = perimeter of base * height

Lateral Surface Area = 26 cm * 9 cm = 234 cm^2.

Calculating the Total Surface Area

The total surface area of the prism is the sum of the base area and the lateral surface area.

Total Surface Area = Base Area + Lateral Surface Area

Total Surface Area = 20 cm^2 + 234 cm^2 = 254 cm^2.

Answer

The total surface area of the prism is 254 cm^2.

Please let me know if I can help you with anything else.