Through the apex of the lower base and the opposite apex of the upper base of a regular quadrangular prism

| September 21, 2021 | education

Through the apex of the lower base and the opposite apex of the upper base of a regular quadrangular prism, a plane is drawn parallel to the diagonals of the bases. Build a section and populate its area, if the side of the base is a, the side edge is b

Through point A, construct a straight line HP parallel to the diagonal BD. Let’s connect points C1 and P, B1 and N. Point K and M are the vertices of the section.

AM = C1K and AM || C1K, AK = C1M and AK || C1M.

Then the section AKC1M is a rhombus.

Diagonal KM = BD = AC = √ (a² + a²) = a * √2 cm.

Diagonal AC1 = √ (AC² + CC1²) = √ (2 * a² + b²) see.

Determine the cross-sectional area. Ssection = KM * AC1 / 2 = a * √2 * √ (2 * a² + b²) / 2 cm2.

Answer: The cross-sectional area is equal to: a * √2 * √ (2 * a² + b²) / 2 cm2.



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