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Find [A'B'C'D'] if [ABCD]=10

Source: 1978 AHSME Problem 29

June 18, 2014
geometrytrigonometryAMC

Problem Statement

Sides AB, BC, CDAB,~ BC, ~CD and DADA, respectively, of convex quadrilateral ABCDABCD are extended past B, C, DB,~ C ,~ D and AA to points B′, C′, D′B',~C',~ D' and A′A'. Also, AB=BB′=6, BC=CC′=7, CD=DD′=8AB = BB' = 6,~ BC = CC' = 7, ~CD = DD' = 8 and DA=AA′=9DA = AA' = 9; and the area of ABCDABCD is 10. The area of A′B′C′D′A 'B 'C'D' is
<spanclass=′latex−bold′>(A)</span>20<spanclass=′latex−bold′>(B)</span>40<spanclass=′latex−bold′>(C)</span>45<spanclass=′latex−bold′>(D)</span>50<spanclass=′latex−bold′>(E)</span>60<span class='latex-bold'>(A) </span>20\qquad<span class='latex-bold'>(B) </span>40\qquad<span class='latex-bold'>(C) </span>45\qquad<span class='latex-bold'>(D) </span>50\qquad <span class='latex-bold'>(E) </span>60
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