Each subsequent rectangle is half the width and height, meaning it's 1/4 the area.
You can express this as a geometric sequence with first term 512, common ratio 1/4, and number of terms 5.
The sum of the geometric sequence is S = 512(1 - 0.25^5)/(1 - 0.25) = 682cm^2.
I have no idea what it means by "do not include cm in your answer", is cm^2 considered including cm? There is no way to express the area without using units given that the areas are in units.
Also, each rectangle’s width is half its height. It can be expressed as w= 1/2h<span> The first rectangle is 32cm tall. Then the measurement would be h=32 w= 1/2h= 16 </span>The first rectangle is 32cm tall and e<span>ach rectangle is half as tall as the previous one. That can be expressed as h(n)= 32(1/2)^n-1
The area of rectangle is area(n)= h*w area(n)=h*</span> (1/2h)= 1/2h ^2 area(n)= 1/2 {32(1/2)^n-1}^2<span> area(n)= 512(1/2)^2n-2
Then the sum of the 5 rectangle would be: </span>area(1) + area(2) + area(3) + area(4)+ area(5) 512(1/2)^2(1)-2 + 512(1/2)^2(2)-2 + 512(1/2)^2(3)-2 + 512(1/2)^2(4)-2 +512(1/2)^2(5)-2 = 512+ 512/4 + 512/16+ 512/ 64 + 512/ 256= 512+ 128 + 32+ 8 + 2= 682
