Question

Найдите площадь боковой поверхности прямоугольного параллелепипеда, стороны основания коαторого равны a и b а диагональ наклонена к плоскости основания под углом α

Answer 1

В основании прямоугольник со сторонами а и в. См рисунок в приложении

Диагональ основания  d находим по теореме Пифагора:

$d= \sqrt{a^2+b^2}$

Из прямоугольного треугольника с острым углом  α

$H= \sqrt{a^2+b^2} \cdot tg \alpha$

S(бок)=Р(осн)·Н=$=2(a+b)\cdot \sqrt{a^2+b^2}\cdot tg \alpha$

Answer 2

Calculating the Lateral Surface Area of a Rectangular Parallelepiped

To find the lateral surface area of a rectangular parallelepiped with base sides of length *a* and *b* and with the diagonal inclined at an angle *α* to the base plane, we can use the following formula:

Lateral Surface Area (A) = 2 * (a + b) * h

Where *h* is the height of the parallelepiped, which can be calculated using the given values of *a*, *b*, and *α*.

Calculating the Height of the Parallelepiped

The height *h* of the parallelepiped can be found using the formula:

h = √(c^2 - (a^2 + b^2) / 4)

Where *c* is the length of the diagonal, which can be calculated using the Pythagorean theorem:

c = √(a^2 + b^2)

Substituting the Values and Calculating

Let's substitute the values of *a*, *b*, and *α* into the formulas to find the lateral surface area of the rectangular parallelepiped.

Given: - Length of the base: *a* - Width of the base: *b* - Angle between the diagonal and the base: *α*

We can calculate the length of the diagonal *c*: c = √(a^2 + b^2)

Then, we can calculate the height *h*: h = √(c^2 - (a^2 + b^2) / 4)

Finally, we can find the lateral surface area *A*: A = 2 * (a + b) * h

Let's proceed with these calculations.