2022 A Individual #20
Source:
April 28, 2022
geometry2022 A Individual
Problem Statement
The area of the dark gray triangle depicted below is , and a segment is divided into lengths and as shown below. What is the area of the light gray triangle? [asy]
size(150);
filldraw((0,0)--(0,12)--(24,-60/7)--cycle, lightgray);
filldraw((14,0)--(14,5)--(0,12)--cycle, gray);
draw((0,0)--(24,0)--(0,12)--cycle);
draw((0,0)--(24,0)--(24,-60/7)--cycle);
draw((0,12)--(24,-60/7));
draw((14,5)--(14,0));
dot((0,0));
dot((0,12));
dot((14,5));
dot((24,0));
dot((14,0));
dot((24,-60/7));
label("", (7,0), S);
label("", (19,0), S);
draw((0,2/3)--(2/3,2/3)--(2/3,0));
draw((14,2/3)--(14+2/3,2/3)--(14+2/3,0));
draw((24-2/3,0)--(24-2/3,-2/3)--(24,-2/3));
[/asy]