To find the area of a trapezoid, we use the formula:
\[ \text{Area} = \frac{(b_1 + b_2)}{2} \times H \]
where \(b_1\) and \(b_2\) are the lengths of the two parallel sides (bases) and \(H\) is the height.
From the numbers you've provided (2 cm, 16 cm, and 7 cm), let's assume:
- \(b_1 = 2 , \text{cm}\)
- \(b_2 = 16 , \text{cm}\)
- \(H = 7 , \text{cm}\)
Now, we can substitute these values into the area formula:
\[ \text{Area} = \frac{(2 + 16)}{2} \times 7 \]
Calculating the bases:
\[ 2 + 16 = 18 \]
Dividing by 2:
\[ \frac{18}{2} = 9 \]
Now, multiply by the height:
\[ 9 \times 7 = 63 \]
Thus, the area of the trapezoid is:
\[ \text{Area} = 63 , \text{cm}^2 \]
Finally, the answer is:
\[ a = 63 , \text{cm}^2 \]