hello,
to find the area of the figure:
A = b x h
b = w ; h = 20-w
A = w(20-w)
A = 20w - w^2 OR A = -w^2+20w
to find the maximum w value:
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
to find the area we substitute all the w's in the equation for 10
A = 20w-w^2
A = 20(10) - (10)^2
A = 200 - 100
A = 100
so to sum up:
the equation for the area is A = 20w - w^2 OR A = -w^2+20w (whichever one should work)
the maxiumum area is 100 square units
hope this helped :)