Question

* This shape is made out of rectangles each 4 units tall; the rectangle at the very bottom is 16 units wide; each next rectangle is half the width of the one below it. There are so many rectangles that the finished drawing would not fit on the page, so you can see that the drawing is incomplete. Calculate the area of the entire shape – even the part that is not drawn.

Answer:
A =
square unit (s)

Answer 1

Answer:

a= SQUARE UNIT...............................................................

Answer 2

128 units

Explanation:

• This question requires us to solve an infinite GP

• As we can see the first unit is 16 wide, then 8, then 4 and so on; this can be written as $64\times (1, 0.5, 0.25, 0.125 ... \infty)$ (64 used as 16*4 = 64 is the area of the first rectangle)

• We have $S_\infty = a/(1-r)$ where a is the first term and r is the common ratio of the GP for summing an infinite GP.

• here we have $a=64 \ \& \ r= 0.5$

• Therefore $S_\infty = \frac{64}{1-0.5} = \frac{64}{0.5} = 128$