MathDB

2

Part of 2001 May Olympiad

Problems(2)

calculations in a right trapezoid

Source: May Olympiad (Olimpiada de Mayo) 2001 L2

9/14/2018
On the trapezoid ABCDABCD , side DADA is perpendicular to the bases ABAB and CDCD . The base ABAB measures 4545, the base CDCD measures 2020 and the BCBC side measures 6565. Let PP on the BCBC side such that BPBP measures 4545 and MM is the midpoint of DADA. Calculate the measure of the PMPM segment.
geometrytrapezoidright angle
folding a rectangle three times, area calculation

Source: May Olympiad (Olimpiada de Mayo) 2001 L1

9/14/2018
Let's take a ABCDABCD rectangle of paper; the side ABAB measures 55 cm and the side BCBC measures 99 cm. We do three folds: 1.We take the ABAB side on the BCBC side and call PP the point on the BCBC side that coincides with AA. A right trapezoid BCDQBCDQ is then formed. 2. We fold so that BB and QQ coincide. A 55-sided polygon RPCDQRPCDQ is formed. 3. We fold again by matching DD with CC and QQ with PP. A new right trapezoid RPCSRPCS. After making these folds, we make a cut perpendicular to SCSC by its midpoint TT, obtaining the right trapezoid RUTSRUTS. Calculate the area of the figure that appears as we unfold the last trapezoid RUTSRUTS.
geometrytrapezoidrectangle