Question

the playground at a park is shaped like a trapezoid. the dimensions of the playground are shown in the diagram. 68 ft, 30 ft, 34 ft, 36 ft. what is the area of the playground in square feet?

Explanation:

Step1: Recall trapezoid area formula

The area \( A \) of a trapezoid is given by \( A=\frac{(b_1 + b_2)h}{2} \), 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).
Here, \( b_1 = 68\) ft, \( b_2 = 36\) ft, and \( h = 30\) ft.

Step2: Substitute values into formula

Substitute \( b_1 = 68 \), \( b_2 = 36 \), and \( h = 30 \) into the formula:
\( A=\frac{(68 + 36)\times30}{2} \)

Step3: Simplify the expression

First, calculate the sum of the bases: \( 68+36 = 104 \)
Then, multiply by the height: \( 104\times30 = 3120 \)
Finally, divide by 2: \( \frac{3120}{2}=1560 \)

Answer:

The area of the playground is \( 1560 \) square feet.