# In an inclined triangular prism, the sides of the base are 5, 6 and 9 cm. The side edge is 10 cm and makes

In an inclined triangular prism, the sides of the base are 5, 6 and 9 cm. The side edge is 10 cm and makes an angle of 45 degrees with the base plane. Find the volume of the prism.

According to Heron’s theorem, we determine the area of the base of the prism.

We calculate the semiperimeter of the triangle ABC: p = (AB + BC + AC) / 2 = (9 + 5 + 6) / 2 = 10 cm.

Savs = √p * (p – AB) * (p – BC) * (p – AC) = √10 * 1 * 5 * 4 = √200 = 10 * √2 cm2.

From the vertex A1, draw a perpendicular A1O to the base ABC, then triangle AA1O is rectangular, in which the angle A1AO = 45. Then AO = A1O.

2 * A1O ^ 2 = AA1 ^ 2 = 100.

A1O ^ 2 = 50.

A1O = 5 * √2 cm.

Then Vpr = Savs * A1O = 10 * √2 * 5 * √2 = 100 cm3. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.