   Chapter 11.4, Problem 41E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Explain why the area of the parallelogram shown is given by the formula (HINT: You will need to use Q N ¯ .) Exercises 41 − 44

To determine

To explain:

The area of the Parallelogram is given by the formula A=absinγ

Explanation

Given,

From the figure,

MN¯=QP¯=b, MQ¯=NP¯=a and M=P=γ

The area of the Parallelogram(A)=The area of the triangle MNQ(A1)+ The area of the triangle QNP(A2)  The area of the triangle MNQ (A1):

For any triangle,

Here, MN¯=b, MQ¯=a and M=γ

The area of the triangle A1=12absinγ

The area of the triangle QNP (A1):

For any triangle,

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