Question

За решение 40 баллов!! Быстрее!!! Основанием прямой призмы служит треугольник со сторонами 10 10 и 12 диагональ меньшей боковой грани составляет с плоскостью основания угол 60 найдите объем призмы

Answer 1

1)∠C1AC=60° AC=10 =>AC1=AC/cos60°=10/0.5=20
2)CC1=$\sqrt{400-100}=\sqrt{300}=10\sqrt{3}$
3)ACB-равнобедренный => СH-высота, медиана и биссектриса 
   AH=HB=6 =>CH=$\sqrt{100-36}= \sqrt{64}=8$
4)Sтреу.=1/2*CH*AB=1/2*8*12=48
5)V=Sтреу.*h=$48*10\sqrt{3} =480 \sqrt{3}$
Ответ $480 \sqrt{3}$

Answer 2

Calculation of the Volume of a Prism

To find the volume of a prism, we need to multiply the area of the base by the height of the prism. In this case, the base of the prism is a triangle with sides measuring 10, 10, and 12, and the diagonal of the smaller lateral face forms a 60-degree angle with the plane of the base.

To calculate the volume, we need to determine the area of the base. Since we have a triangle, we can use Heron's formula to find the area. Heron's formula states that the area of a triangle with sides 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

Let's calculate the area of the base using the given side lengths of the triangle:

a = 10, b = 10, c = 12

s = (10 + 10 + 12) / 2 = 16

Area = sqrt(16 * (16 - 10) * (16 - 10) * (16 - 12)) = sqrt(16 * 6 * 6 * 4) = sqrt(2304) = 48

Now that we have the area of the base, we can calculate the volume of the prism by multiplying the area by the height. However, the height of the prism is not given in the question. Without the height, we cannot determine the volume of the prism.

Please provide the height of the prism so that we can calculate the volume accurately.