Question

four sections of forest are described in the table with the number of trees in each section. what is the population density in order from least to greatest? section a b c d shape a rectangle with a length of 60 miles and a width of 75 miles a right triangle with legs 60 miles and 70 miles a square with side length of 60 miles a trapezoid with bases of 50 miles and 70 miles and a height of 50 miles number of trees 450,000 250,000 400,000 350,000

Explanation:

Step1: Calculate area of rectangle in Section A

The area formula for a rectangle is $A = l\times w$. Given $l = 60$ miles and $w=75$ miles, so $A_A=60\times75 = 4500$ square - miles. The population density $D_A=\frac{4500000}{4500}=1000$ trees per square - mile.

Step2: Calculate area of right - triangle in Section B

The area formula for a right - triangle is $A=\frac{1}{2}ab$. Given $a = 60$ miles and $b = 70$ miles, so $A_B=\frac{1}{2}\times60\times70=2100$ square - miles. The population density $D_B=\frac{2500000}{2100}\approx1190.48$ trees per square - mile.

Step3: Calculate area of square in Section C

The area formula for a square is $A = s^2$. Given $s = 60$ miles, so $A_C=60\times60 = 3600$ square - miles. The population density $D_C=\frac{4000000}{3600}\approx1111.11$ trees per square - mile.

Step4: Calculate area of trapezoid in Section D

The area formula for a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$. Given $b_1 = 50$ miles, $b_2 = 70$ miles and $h = 50$ miles, so $A_D=\frac{(50 + 70)\times50}{2}=3000$ square - miles. The population density $D_D=\frac{3500000}{3000}\approx1166.67$ trees per square - mile.

Step5: Order the densities

Comparing the densities: $D_A = 1000$, $D_B\approx1190.48$, $D_C\approx1111.11$, $D_D\approx1166.67$. The order from least to greatest is $A, C, D, B$.

Answer:

A, C, D, B