If i am putting carpet in my basement, how many square feet of carpeting do i need if the room is 20ft. x10ft.?

It would be: 20* 10 = 200 ft²

so, the carpet should have the area of about 200 ft²

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