1. Let's analyze the top-left shape where the circle is connected to rectangles and hearts: Each heart shape's number ($3$ and $4$) is connected to the circle labeled $2$, which, in turn, connects to rectangle $16$. 2. Notice the triangle inside the top-left circle has sides labeled $2$, $1$, and $4$, and the rectangle inside it has number $7$. 3. Considering the pattern from the two hearts to the circle, and then to the rectangle numbers, check multiplication or addition: - From hearts to circle: $3 \times 4 = 12$; given as $2$, possibly a factor or sum relation. - From circle to rectangle: $2 \times 8 = 16$. 4. For the top-right shape with hearts labeled $2$ and $4$, circle $3$, and rectangle $18$: - $2 \times 4 = 8$, circle is $3$, rectangle $18$. - $3 \times 6 = 18$. 5. For bottom-left, hearts $2$ and $2$, circle $5$, rectangle is blank: - $2 \times 2 = 4$, circle $5$. - Using previous pattern: rectangle $= circle \times ?$ 6. For bottom-right, hearts blank and $2$, circle $7$, rectangle $49$: - Since rectangle is $49$, which is $7^2$, and circle is $7$, probably rectangle $= circle^2$. 7. Using the bottom-right deduction, rectangle is circle squared. 8. Check if rectangle $= circle^2$ for the other known rectangles: - Top-left: circle $2$, rectangle $16$; $16 = 2^4$, not square. - Top-right: circle $3$, rectangle $18$; $18$ not $3^2=9$, pattern may differ. 9. The triangle numbers in top-left circle are $2$, $1$, $4$; rectangle inside circle is $7$. - Note $2 + 1 + 4 = 7$. 10. Top-right triangle sides $2$, $9$, $25$; rectangle $12$ inside circle: - $2 + 9 + 25 = 36$, no match with $12$. 11. Bottom-left triangle $3,4,9$, rectangle blank: - $3 + 4 + 9 = 16$, likely rectangle value is $16$. 12. Bottom-right triangle $7,121,81$, rectangle blank: - $7 + 121 + 81 = 209$, likely rectangle value is $209$. Final answers: - Bottom-left rectangle = $16$ - Bottom-right rectangle = $209$ Summary: - The rectangles inside the circles seem to be the sum of the triangle side numbers. - The rectangles below the circles differ by pattern; bottom-right rectangle is circle squared. Hence, Bottom-left rectangle value: $16$ Bottom-right rectangle value: $49$ given outside, but inside sum is $209$ for triangle; the rectangle below circle (bottom-right) is $49$ matching $7^2$.