Final answer:
To calculate the population of a given triangle region, the area of the triangle is found using the formula (1/2 × base × height) and then multiplied by the population density. For a 3-mile base and 7-mile height with a density of 678 people per square mile, the population is 7119.
Step-by-step explanation:
The student has asked about calculating the population of a triangle region given its base, height, and population density. To determine the population, we must first calculate the area of the triangle using the formula, which is 1/2 × base × height. Here, the base of the triangle is 3 miles and the height is 7 miles. So, the area is 1/2 × 3 miles × 7 miles = 10.5 square miles. Next, we multiply the area by the population density, which is 678 people per square mile, to find the total population. Hence, the population is 10.5 square miles × 678 people per square mile = 7119 people.