area of a ... square inside a square wanted (Chile 2018 L2 P1)
Source:
October 22, 2022
geometrysquareareas
Problem Statement
Consider a square of side . Points are chosen on sides , , and respectively such that , with . The segments , , and are drawn. Calculate the area of the quadrilateral that is formed in the center of the figure.[asy]
unitsize(1 cm);pair A, B, C, D, P, Q, R, S;A = (0,3);
B = (0,0);
C = (3,0);
D = (3,3);
P = (0,2);
Q = (1,0);
R = (3,1);
S = (2,3);draw(A--B--C--D--cycle);
draw(A--Q);
draw(B--R);
draw(C--S);
draw(D--P);label("", A, NW);
label("", B, SW);
label("", C, SE);
label("", D, NE);
label("", P, W);
label("", Q, dir(270));
label("", R, E);
label("", S, N);
label("", (A + P)/2, W);
label("", (B + Q)/2, dir(270));
label("", (C + R)/2, E);
label("", (D + S)/2, N);
[/asy]