# Write a system of inequalities to describe the shaded figure in the picture here: http://i91.photobucket.com/albums/k305/Suger_Pie/dafds.jpgI honestly dont know how to do this problem, so can you...

Write a system of inequalities to describe the shaded figure in the

picture here:

http://i91.photobucket.com/albums/k305/Suger_Pie/dafds.jpg

I honestly dont know how to do this problem, so can you explain it to me step by step? Thank you,

neela | High School Teacher | (Level 3) Valedictorian

Posted on

At the site below,

we notice a trapezium whose base is streteched  equally about the origin 3 units on either sides of the origin along the  x axis.

If we go up from along the y axis by 3 units we see the other parallel side of the trapezium which streches by 2 units on either side of the y axis (perpenducular to y axis and || to x axis.

The shade part is the area of the trapezium  with vertices at A(-3 , 0) , B(3,0), C(2 , 3) and D(-2,3).

The area of the trapezium = (1/2)(sum of parallel sides)(distance between the paralle sides) = (1/2){(3+3)+(2+2)}(3) =15.

The inequality here we can try to make out  is :

Area of  the trapezium ABCD  < area of the outer rectangle with vertices at (-3,0) , (3,0), ( 3,3) and (-3,3) = 6*3 = 18 sq unit.

The area of the trapezium ABCD > Area of the inner rectangle  with vertices at (-2,0) ,(2,0), (2,3) and (-2,3) =  4*3 = 12 sqrt.

Of course the average of are  inner and outer rectangles = (18+12)/2 = 15 sq units = area of the trapezium ABCD.