Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

geometry intermediate

Problem

The shaded region consists of 16 congruent squares. If cm, what is the area of the entire shaded region?

problem
Solution
Imagine the square whose diagonal would be PQ. Clearly, that square would be formed of 9 of the shaded squares. The formula for the area of a square from its diagonal is , therefore, the area of that imaginary square is 18. Thus, each smaller shaded square has area 2, making for a total of for the entire shaded area.
Final answer
32\text{ square cm}