Questions: What is the area of the given trapezoid ABCD? A. 110 in^2 B. 112 in^2 C. 28 in^2 D. 56 in^2

Solution Steps

The area \( A \) of a trapezoid can be calculated using the formula: \[ A = \frac{1}{2} \times (b_1 + b_2) \times h \] where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases) and \( h \) is the height.

In the given trapezoid \( ABCD \):

• \( b_1 = 6 \) inches (length of the top base \( AB \))
• \( b_2 = 22 \) inches (length of the bottom base \( DC \))
• \( h = 4 \) inches (height from \( D \) to \( AB \))

Substitute these values into the formula: \[ A = \frac{1}{2} \times (6 + 22) \times 4 \]

First, add the lengths of the bases: \[ 6 + 22 = 28 \]

Next, multiply by the height: \[ 28 \times 4 = 112 \]

Finally, multiply by \( \frac{1}{2} \): \[ \frac{1}{2} \times 112 = 56 \]

Final Answer