Find the area of a trapezoid with a base of $27 \mathrm{~cm}$, a height of $3 \mathrm{~cm}$, and top of $16 \mathrm{~cm}$.

Step 1 ：Given a trapezoid with a base of \(27 \mathrm{~cm}\), a height of \(3 \mathrm{~cm}\), and top of \(16 \mathrm{~cm}\).

Step 2 ：The area of a trapezoid can be calculated using the formula: Area = \(\frac{1}{2} \times (base1 + base2) \times height\)

Step 3 ：Substitute the given values into the formula: base1 = \(27 \mathrm{~cm}\), base2 = \(16 \mathrm{~cm}\), and height = \(3 \mathrm{~cm}\).

Step 4 ：Calculate the area: \(\frac{1}{2} \times (27 + 16) \times 3 = 64.5 \mathrm{~cm}^2\).

Step 5 ：Final Answer: The area of the trapezoid is \(\boxed{64.5} \mathrm{~cm}^2\).