A hang glider is soaring over a 100-acre area that consists of thick forest and open fields. In the diagram below, the forested area is shaded in green and the open field is the white space. Upon landing, the hang glider realizes she has dropped her keys.

Question

A trapezoid is split into 3 sections. The bottom section is 35 acres, the middle section is 20 acres, and the top section is 45 acres. The top and bottom sections are shaded.

What is the probability that her keys have landed within the forest?

0.2
0.6
0.8
1.0

Answer 1

To find the probability that the keys have landed within the forest, we first need to determine the area of the forest within the specified trapezoid.

According to the information provided:

• The total area of the trapezoid is \(35 \text{ acres} + 20 \text{ acres} + 45 \text{ acres} = 100 \text{ acres}\).
• The shaded areas (forest), which are represented by the top and bottom sections of the trapezoid, comprise \(35 \text{ acres} + 45 \text{ acres} = 80 \text{ acres}\).

Now we can calculate the probability that the keys landed in the forest:

\[ \text{Probability (keys in forest)} = \frac{\text{Area of forest}}{\text{Total area}} = \frac{80 \text{ acres}}{100 \text{ acres}} = 0.8 \]

Thus, the probability that the keys have landed within the forest is \(0.8\).

The correct answer is \(0.8\).