hello,
<u><em>to find the area of the figure:</em></u>
A = b x h
b = w ; h = 20-w
A = w(20-w)
A = 20w - w^2 OR A = -w^2+20w
<u><em>to find the maximum w value:</em></u>
so this equation when graphed would make a parabola. the maximum area is found using the vertex of the parabola.
you can graph it to find the vertex or the vertex can be found with the formula -b/2a
our b is 20 and our a is -1
-b/2a = -20/2(-1) = 10
10 is the w value
<u><em>to find the area we substitute all the w's in the equation for 10</em></u>
A = 20w-w^2
A = 20(10) - (10)^2
A = 200 - 100
A = 100
<u><em>so to sum up:</em></u>
the equation for the area is <u>A = 20w - w^2 </u><u>OR</u><u> A = -w^2+20w</u> (whichever one should work)
the maxiumum area is <u>100</u> square units
hope this helped :)
