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3D Geometry Problem

Source: 1989 National High School Mathematics League, Exam One, Problem 14

February 25, 2020
geometry3D geometrypyramid

Problem Statement

In regular triangular pyramid S−ABCS-ABC, hieght SO=3SO=3, length of sides of bottom surface is 66. Projection of AA on plane SBCSBC is O′O'. P∈AO′,APPO′=8P\in AO',\frac{AP}{PO'}=8. Draw a plane parallel to plane ABCABC and passes PP. Find the area of the cross section.
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