Question

a field is shaped like a trapezoid with the dimensions shown. what is the area of the field? 150 yd, 200 yd, 300 yd (the image shows a right trapezoid with right angles at a and b, top base bc = 150 yd, bottom base ad = 300 yd, height ab = 150 yd, and side cd = 200 yd)

Explanation:

Step1: Recall trapezoid area formula

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

Step2: Identify values from the diagram

From the figure: $b_1 = 150$ yd, $b_2 = 300$ yd, $h = 250$ yd.

Step3: Substitute values into formula

$$\text{Area} = \frac{1}{2} \times (150 + 300) \times 250$$

Step4: Calculate sum of the bases

$150 + 300 = 450$

Step5: Compute final area

$$\text{Area} = \frac{1}{2} \times 450 \times 250 = 225 \times 250 = 56250$$

Answer:

56250 square yards