Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 8 - Section 8.2 - Perimeter and Area of Polygons - Exercises - Page 369: 4

Answer

28 units

Work Step by Step

Using pythagoras theorem in right triangle OCF $OC^{2}$ =$OF^{2}$ + $FC^{2}$ $5^{2}$ = $4^{2}$ + $FC^{2}$ $FC^{2}$ = $5^{2}$- $4^{2}$ $FC^{2}$ = 25 -16 $FC^{2}$ = 9 FC = 3 In rectangle ABCD CF = FD, BE = EC because it is given that OE is perpendicular to BC and OF is perpendicular to CD, So OE and OF bisects BC and CD CD = CF +FD = 3+3 = 6 BC = BE + EC= 4+4 = 8 In a parallelogram opposite sides are equal therefore AB = CD= 6, AD = BC = 8 The perimeter of ABCD parallelogram is AB+BC+CD+AD = 6+8+6+8 = 28 units.
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