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 bases, and \( H \) is the height of the trapezoid.
From your information:
- The lengths given are 2 cm, 7 cm, and 16 cm. It seems that you might be indicating the bases and height, but we need to specify which lengths correspond to the bases and which is the height.
Assuming:
- \( b_1 = 2 , \text{cm} \) (the shorter base),
- \( b_2 = 7 , \text{cm} \) (the longer base),
- \( H = 16 , \text{cm} \) (the height),
Now we can substitute these values into the area formula:
\[ \text{Area} = \frac{(2 , \text{cm} + 7 , \text{cm})}{2} \times 16 , \text{cm} \] \[ = \frac{9 , \text{cm}}{2} \times 16 , \text{cm} \] \[ = 4.5 , \text{cm} \times 16 , \text{cm} \] \[ = 72 , \text{cm}^2 \]
So, the area of the trapezoid is:
\[ a = 72 , \text{cm}^2 \]