Question

find the area of this trapezoid. be sure to include the correct unit in your answer.

Explanation:

Step1: Recall trapezoid area formula

The area \( A \) of a trapezoid is given by \( A = \frac{1}{2}(b_1 + b_2)h \), where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases), and \( h \) is the height (the perpendicular distance between the bases).

Step2: Identify \( b_1 \), \( b_2 \), and \( h \)

From the diagram, the two parallel sides (bases) are \( b_1 = 13 \, \text{ft} \) and \( b_2 = 7 \, \text{ft} \), and the height \( h = 5 \, \text{ft} \).

Step3: Substitute values into the formula

Substitute \( b_1 = 13 \), \( b_2 = 7 \), and \( h = 5 \) into the formula:

$$ A = \frac{1}{2}(13 + 7) \times 5 $$

Step4: Simplify the expression

First, add the bases: \( 13 + 7 = 20 \). Then, multiply by \( \frac{1}{2} \): \( \frac{1}{2} \times 20 = 10 \). Finally, multiply by the height: \( 10 \times 5 = 50 \).

Answer:

\( 50 \, \text{square feet} \) (or \( 50 \, \text{ft}^2 \))