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

July 29, 2021 | education

| **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.

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