In a straight triangular prism, a plane is drawn through one of the sides of the base, intersecting the opposite lateral

| March 19, 2021 | education

In a straight triangular prism, a plane is drawn through one of the sides of the base, intersecting the opposite lateral edge and deviated from the base plane by 45 degrees. The base area is Q. Determine the cross-sectional area.

We draw the height AH at the base of the prism and connect the point H with the point K – the point of intersection of the rib BB1 and the section of the ВCК. The formed linear angle AНC is the angle between the section plane and the base of the prism.

The base of the prism is the orthogonal projection of the ВCК triangle.

Then the ratio of the area of the triangle ACB to the plane of the triangle BCK is the cosine of the angle between them.

Cos45 = Savs / Svsk.

Svsk = Savs / Cos45 = Q / (√2 / 2) = 2 * Q / √2 = Q * √2 cm2.

Answer: The cross-sectional area is Q * √2 cm2.



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