Question

question 1
the triangular section labeled forest on the map represents a forested area along the walking path. each grid square represents 100 feet by 100 feet.
using the coordinates of the triangles vertices shown on the map, which value represents the area of the forest?
a. 160,000 square feet
b. 240,000 square feet
c. 320,000 square feet
d. 630,000 square feet
question 2
the entrance to the park is at the origin. a person begins at the entrance walks along the walking path, following each connected segment in order until reaching point w on the map. using the coordinates shown on the diagram and rounding to the nearest hundred feet. what is the approximate total distance the person walked?

Explanation:

Step1: Determine the base and height of the forest triangle

Assume the base of the forest triangle \(b = 16\) grid - units and the height \(h= 30\) grid - units (by counting the number of grid - squares). Since each grid square is \(100\) feet by \(100\) feet, the actual base \(B = 16\times100=1600\) feet and the actual height \(H = 30\times100 = 3000\) feet.

Step2: Use the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}\times B\times H\). Substitute \(B = 1600\) feet and \(H = 3000\) feet into the formula:

$$A=\frac{1}{2}\times1600\times3000$$

$$A = 800\times3000$$

$$A=2400000$$

square - feet

Answer:

B. 240,000 square feet