Trapezoid Area Calculation: Finding Area with Heights 5 and Bases 8 and 13

What is the area of the trapezoid in the diagram?

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

• Step 1: Identify the given dimensions of the trapezoid.
• Step 2: Apply the area formula for a trapezoid using these dimensions.
• Step 3: Perform the calculation to determine the area.

Let's work through each step more clearly:
Step 1: From the problem, we identify that the trapezoid has one base $b_1 = 13$ units, another base $b_2 = 8$ units, and its height $h = 5$ units.
Step 2: The formula for the area of a trapezoid is:

$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Step 3: Substitute the values into the formula:

$A = \frac{1}{2} \times (13 + 8) \times 5$

$A = \frac{1}{2} \times 21 \times 5$

$A = \frac{1}{2} \times 105$

$A = 52.5 \, \text{units}^2$

Therefore, the area of the trapezoid is $52.5 \, \text{units}^2$.