In a random survey of 250 students, 70 were in the school band. if the total student population is 1500 students, how many students are in the band?

This is a proportion problem. Start by setting up your two fractions (part over whole) and then cross multiplying

First, multiply

70 x 1500 = 105, 000

Now divide

105,000/ 250 = 420

Answer is 420

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2