Question

В наклонной треугольной призме стороны основания 5, 6 и 9 см. Боковое ребро равно 10 см и составляет с плоскостью основания угол в 45 гр. Найти объём призмы

Answer 1

Площадь основания найдём по формуле Герона\
р =(9+6+5) \ 2= 10 тода S = √10*1*4*5 = 10√2
Пусть боковое ребро АК =10. Опустим из точки К высоту КМ на основание Тогда из прямоугольного тр-ка АКМ 
КМ= 10* sin45 = 5√2
объём призмы.= 10√2* 5√2 =100 куб см

Answer 2

Calculation of the Volume of the Prism

To find the volume of the inclined triangular prism, we can use the formula:

Volume = (Area of the base) x (Height)

First, let's calculate the area of the base. Since the base of the prism is a triangle, we can use Heron's formula to find its area.

Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:

Area = sqrt(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 5 cm, 6 cm, and 9 cm. Let's calculate the area of the base using Heron's formula:

s = (5 + 6 + 9) / 2 = 10

Area = sqrt(10(10-5)(10-6)(10-9)) = sqrt(10 * 5 * 4 * 1) = sqrt(200) cm^2

Now, we need to find the height of the prism. The height is the perpendicular distance between the base and the opposite face. In this case, the height is equal to the length of the inclined edge.

Given that the length of the inclined edge is 10 cm, the height of the prism is also 10 cm.

Now, we can calculate the volume of the prism:

Volume = (Area of the base) x (Height) = sqrt(200) cm^2 x 10 cm = 10 sqrt(200) cm^3

Therefore, the volume of the inclined triangular prism is 10 sqrt(200) cm^3.

Please note that the calculations provided above are based on the given information and assumptions.