To find the missing measurement (the bottom), we can use the formula for the area of a trapezoid since we have two parallel sides (the top and bottom measurements) and the height (the middle measurement). The area of a trapezoid is given by the formula:
\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]
In this case:
- Base₁ (top) = 6.9 cm
- Base₂ (bottom) = unknown (let's call it \( b \))
- Height (middle) = 6.3 cm
- Area = 30.9 cm²
Plugging in the values into the area formula:
\[ 30.9 = \frac{1}{2} \times (6.9 + b) \times 6.3 \]
First, multiply both sides of the equation by 2 to eliminate the \(\frac{1}{2}\):
\[ 61.8 = (6.9 + b) \times 6.3 \]
Next, divide both sides by 6.3:
\[ \frac{61.8}{6.3} = 6.9 + b \]
Calculating the left side:
\[ 9.8 = 6.9 + b \]
Now, solve for \( b \):
\[ b = 9.8 - 6.9 = 2.9 \]
Thus, the missing measurement (bottom) is:
2.9 cm
So the answer from the options provided is:
2.9 cm