To find the missing measurement (the bottom), we will use the formula for the area of a trapezoid:
\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]
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, we can rearrange the formula to solve for \( b_2 \):
\[ 30.9 = \frac{1}{2} \times (6.9 + b_2) \times 6.3 \]
First, simplify the equation:
\[ 30.9 = (6.9 + b_2) \times 3.15 \]
Now divide both sides by 3.15:
\[ \frac{30.9}{3.15} = 6.9 + b_2 \]
Calculating the left side:
\[ \frac{30.9}{3.15} \approx 9.8 \]
Now we have:
\[ 9.8 = 6.9 + b_2 \]
Subtracting 6.9 from both sides gives:
\[ b_2 = 9.8 - 6.9 = 2.9 \]
So, the missing measurement for the bottom is:
\[ b_2 \approx 2.9 , \text{cm} \]
Thus, the answer is 2.9 cm.