Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 8 - Section 8.1 - Area and Initial Postulates - Exercises - Page 350: 31

Answer

24$cm^{2}$

Work Step by Step

Given $A_{RSTV}$ = 48 $cm^{2}$ X is the midpoint of VT and Y is the midpoint of TS Therefore VX = XT and TY=YS Lets join RT In triangle VRT, $A_{VRX}$ = $A_{VXT}$ In triangle RTS, $A_{RTY}$ = $A_{RYS}$ Because “A median of a triangle separates it into two triangles of equal area.” $A_{RSTV}$ = $A_{VRX}$ + $A_{RXT}$ + $A_{RTY}$ + $A_{RYS}$ = $A_{RXT}$ + $A_{RXT}$ + $A_{RTY}$ + $A_{RTY}$ = 2 $A_{RXT}$ + 2 $A_{RTY}$ = 2($A_{RXT}$ + $A_{RTY}$) = 2 $A_{RXTY}$ 48 = 2 $A_{RXTY}$ $A_{RXTY}$ = $\frac{48}{2}$ = 24$cm^{2}$
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