Calculate Trapezoid Area: Finding Area with Heights 3 and Parallel Sides 4 and 7

What is the area of the trapezoid in the diagram below?

To determine the area of the trapezoid, we will follow these steps:

• Step 1: Identify the provided dimensions of the trapezoid.
• Step 2: Apply the formula for the area of a trapezoid.
• Step 3: Perform the arithmetic to calculate the area.

Let's proceed through these steps:

Step 1: Identify the dimensions
The given dimensions from the diagram are:
Height $h = 3$ cm.
One base $b_1 = 4$ cm.
The other base $b_2 = 7$ cm.

Step 2: Apply the area formula
To find the area $A$ of the trapezoid, use the formula:
$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Step 3: Calculation
Substituting the known values into the formula:
$A = \frac{1}{2} \times (4 + 7) \times 3$

Simplify the expression:
$A = \frac{1}{2} \times 11 \times 3$

Calculate the result:
$A = \frac{1}{2} \times 33 = \frac{33}{2} = 16.5$ cm²

The area of the trapezoid is therefore $16.5$ cm².

Given the choices, this corresponds to choice : $16.5$ cm².

Therefore, the correct solution to the problem is $16.5$ cm².