To find the missing measurement at the bottom, we can use the formula for the area of a trapezoid, which is given by:
\[ \text{Area} = \frac{(b_1 + b_2)}{2} \times h \]
Where:
- \( b_1 \) is the length of the top base (6.9 cm)
- \( b_2 \) is the length of the bottom base (unknown)
- \( h \) is the height (6.3 cm)
- Area is given as (30.9 cm²)
Plugging in the known values:
\[ 30.9 = \frac{(6.9 + b_2)}{2} \times 6.3 \]
To simplify, first divide both sides by 6.3:
\[ \frac{30.9}{6.3} = \frac{(6.9 + b_2)}{2} \]
Calculating \( \frac{30.9}{6.3} \):
\[ \frac{30.9}{6.3} \approx 4.9 \]
Now, we have:
\[ 4.9 = \frac{(6.9 + b_2)}{2} \]
Next, multiply both sides by 2:
\[ 9.8 = 6.9 + b_2 \]
Now, solve for \( b_2 \):
\[ b_2 = 9.8 - 6.9 \]
Calculating that gives:
\[ b_2 = 2.9 , \text{cm} \]
Therefore, the missing measurement at the bottom is:
\[ \boxed{2.9 , \text{cm}} \]