Question

В основании прямого параллелепипеда- ромб с острым углом 30. Боковое ребро равно 5 дм, а полная поверхность параллелепипеда 96 дм.кв. Найдите боковую поверхность параллелепипеда.

Answer 1

S ромба = a^2 * sin α = 5*5*sin 30° = 25 * 1/2 (дм^2) - площадь основания
2 * S ромба = 2 * 25 * 1/2 = 25 (дм^2) – площадь двух оснований
S бок.пов. = S пов.паралл. – 2 * S осн. = 96 – 25 = 71 дм^2

Answer 2

Calculation of the lateral surface area of a parallelepiped

To find the lateral surface area of a parallelepiped, we need to know the length of one of the lateral edges and the total surface area of the parallelepiped.

Given information: - The lateral edge of the parallelepiped is 5 dm. - The total surface area of the parallelepiped is 96 dm².

To calculate the lateral surface area, we can use the formula:

Lateral Surface Area = Total Surface Area - 2 * (Area of the base)

Since the parallelepiped is a rhombus with an acute angle of 30 degrees, we can calculate the area of the base using the formula:

Area of the base = (lateral edge)² * sin(angle)

Let's calculate the lateral surface area step by step.

1. Calculate the area of the base: - Lateral edge = 5 dm - Angle = 30 degrees

Using the formula for the area of a rhombus, we have:

Area of the base = (5 dm)² * 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.

Area of the base = (5 dm)² * 0.5

2. Calculate the lateral surface area: - Total surface area = 96 dm² - Area of the base = (5 dm)² * 0.5

Using the formula for the lateral surface area, we have:

Lateral Surface Area = 96 dm² - 2 * [(5 dm)² * 0.5]

Let's calculate the values:

Lateral Surface Area = 96 dm² - 2 * (25 dm² * 0.5) Lateral Surface Area = 96 dm² - 2 * 12.5 dm² Lateral Surface Area = 96 dm² - 25 dm² Lateral Surface Area = 71 dm²

Therefore, the lateral surface area of the parallelepiped is 71 dm².