   Chapter 8.1, Problem 32E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# For Exercise 31 and 32, X is the midpoint of V T ¯ and Y is the midpoint of T S ¯ . If A R Y T X = 13.5  in 2 , find A R S T V . To determine

To find:

ARSTV If ARYTX=13.5 in2.

Explanation

“A median of a triangle separated it into two triangles of equal area”.

Calculation:

Given,

Area of RYTX(A)=13.5 in2

Draw a diagonal RT¯ in RSTV which separates RSTV into two triangle RVT and RVT

In RVT X is the midpoint of VT¯ from R

(i.e.) RX is the median of RVT since, “A median of a triangle separated it into two triangles of equal area”

(i.e.)RX¯ separates the RVT into RXV and RXT with equal area,

ARXV=ARXT

In RTS,Y is the midpoint of TS¯ from R.

(i.e.) RY¯ is the median of RTS

RY¯ separates the RTS into RYT and RYS with equal area,

ARYT=ARYS

Now, the figure becomes,

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