To find the area of the trapezoid, we need the lengths of the two bases (B¹ and B²) and the height (H).
From the dimensions you've given (5 cm, 27 cm, and 19 cm), we can assume:
- Base 1 (B¹) = 27 cm
- Base 2 (B²) = 5 cm
- Height (H) = 19 cm
Now we can use the formula for the area of a trapezoid:
\[ \text{Area} = \frac{(B^1 + B^2)}{2} \times H \]
Substituting the values:
\[ \text{Area} = \frac{(27 , \text{cm} + 5 , \text{cm})}{2} \times 19 , \text{cm} \]
First, calculate \(B^1 + B^2\):
\[ 27 , \text{cm} + 5 , \text{cm} = 32 , \text{cm} \]
Now, plug it back into the area formula:
\[ \text{Area} = \frac{32 , \text{cm}}{2} \times 19 , \text{cm} = 16 , \text{cm} \times 19 , \text{cm} \]
Now, calculate:
\[ 16 \times 19 = 304 \]
Thus, the area \(a\) of the trapezoid is:
\[ a = 304 , \text{cm}² \]