Complementary Counting
Source: 2021 Fall AMC 10/12 B #2
November 17, 2021
complementary countingAMC 12 BAMC 10 BAMCAMC 10AMC 12
Problem Statement
What is the area of the shaded figure shown below?[asy]
size(200);
defaultpen(linewidth(0.4)+fontsize(12));
pen s = linewidth(0.8)+fontsize(8);pair O,X,Y;
O = origin;
X = (6,0);
Y = (0,5);
fill((1,0)--(3,5)--(5,0)--(3,2)--cycle, palegray+opacity(0.2));
for (int i=1; i<7; ++i)
{
draw((i,0)--(i,5), gray+dashed);
label("", (i,0), 2*S);
if (i<6)
{
draw((0,i)--(6,i), gray+dashed);
label("", (0,i), 2*W);
}
}
label("", O, 2*SW);
draw(O--X+(0.15,0), EndArrow);
draw(O--Y+(0,0.15), EndArrow);
draw((1,0)--(3,5)--(5,0)--(3,2)--(1,0), black+1.5);
[/asy]