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computational, papefolding a square to get a nonagon

Source: 2013 (-14) Swedish Mathematical Competition p2

August 31, 2020
geometrypaperfoldingnonagonsquare

Problem Statement

The paper folding art origami is usually performed with square sheets of paper. Someone folds the sheet once along a line through the center of the sheet in orde to get a nonagon. Let pp be the perimeter of the nonagon minus the length of the fold, i.e. the total length of the eight sides that are not folds, and denote by s the original side length of the square. Express the area of the nonagon in terms of pp and ss.