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 8.1 - Area and Initial Postulates - Exercises - Page 360: 32

Answer

27 $in^{2}$

Work Step by Step

Given $A_{RYTX}$ = 13.5 $in^{2}$ 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 $A_{RXTY}$ $A_{RSTV}$ = 2 * 13.5 $A_{RSTV}$ = 27 $in^{2}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.