Question

what is the area of the trapezoid? 12 cm, 17 cm, 15 cm, 17 cm, 28 cm, square centimeters

Explanation:

Step1: Recall the formula for the area of a trapezoid

The formula for the area \( A \) of a trapezoid is \( A=\frac{(a + b)}{2}\times h \), where \( a \) and \( b \) are the lengths of the two parallel sides (bases), and \( h \) is the height (the perpendicular distance between the bases).

Step2: Identify the values of \( a \), \( b \), and \( h \)

From the diagram, the lengths of the two parallel sides are \( a = 12\space\text{cm} \) and \( b = 28\space\text{cm} \), and the height \( h = 15\space\text{cm} \).

Step3: Substitute the values into the formula

First, calculate the sum of the bases: \( a + b=12 + 28 = 40\space\text{cm} \).
Then, divide this sum by 2: \( \frac{a + b}{2}=\frac{40}{2}=20\space\text{cm} \).
Finally, multiply this result by the height: \( A = 20\times15=300\space\text{cm}^2 \).

Answer:

300