1. Let's analyze the patterns for each triangle inside the circles. 2. Top-left triangle: The numbers are 2 (top-left), 1 (top-right), 4 (bottom), and 7 (rectangle). - Notice that $2^2=4$, matching the bottom number. - The rectangle number is 7; observe $2+1+4=7$. 3. Top-right triangle: Numbers 2, 9, 25, and 12. - Check squares: $2^2=4$, $9^2=81$, $25^2=625$, which do not directly relate. - Sum $2+9+25=36$ unlike 12. - Test product: $2\times 9\times 25=450$; no direct link. - Try sum of digits $2+9+2+5=18$, no match. - Look for relation between 12 and given numbers: $12=2+9+1$ (approximation no). - Alternatively, see if $12$ is average: $(2+9+25)/3=12$ exactly. 4. Bottom-left triangle: 3, 4, 9, rectangle empty. - $3^2=9$ matches bottom. - $3+4=7$, rectangle empty suggests 7? 5. Bottom-right triangle: 7, 121, 81, rectangle empty. - $7^2=49$ does not match 121 or 81. - $11^2=121$ and $9^2=81$. - The top-right and bottom numbers are perfect squares: $11^2=121$, $9^2=81$. - Sum of 7 and unknown rectangle possibly relates? 6. Summary: - For triangles, bottom number usually relates to square of one of the top numbers. - Rectangle number may be sum of the three or average (as in second triangle). 7. Overall logic: - Bottom number often equals square of top-left number. - Rectangle number is sum (or average) of the triangle numbers. Therefore: - Top-left rectangle = sum $2+1+4=7$ (given 7) - Top-right rectangle = average $(2+9+25)/3=12$ (given 12) - Bottom-left rectangle = sum $3+4+9=16$ (empty, logical rectangle is 16) - Bottom-right rectangle = sum $7+121+81=209$ (empty, logical rectangle is 209) Final answers: - Bottom-left rectangle number: 16 - Bottom-right rectangle number: 209