1998 AJHSME Problems/Problem 13

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Problem 13

What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale)

[asy] draw((0,0)--(0,4)--(4,4)--(4,0)--cycle); draw((0,0)--(4,4)); draw((0,4)--(3,1)--(3,3)); draw((1,1)--(2,0)--(4,2)); fill((1,1)--(2,0)--(3,1)--(2,2)--cycle,black); [/asy]

$\text{(A)}\ \dfrac{1}{6} \qquad \text{(B)}\ \dfrac{1}{7} \qquad \text{(C)}\ \dfrac{1}{8} \qquad \text{(D)}\ \dfrac{1}{12} \qquad \text{(E)}\ \dfrac{1}{16}$

Solution

We can divide the large square into quarters by diagonals.

Then, in $\frac{1}{4}$ the area of the big square, the little square would have $\frac{1}{2}$ the area.

$\frac{1}{4}\times\frac{1}{2}=\frac{1}{8}=\boxed{C}$


See also

1998 AJHSME (ProblemsAnswer KeyResources)
Preceded by
1997 AJHSME
Followed by
1999 AMC 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions