Math Help - Circumscribed/inscribed area problem

1. Circumscribed/inscribed area problem

I've attached the homework problem I'm having.

My biggest issue is getting it into sigma notation to use the summation rules on it. At least I think that's where my failure is.

I really need to see this or a similar problem worked out entirely using sigma notation. The homework does not use sigma notation but instead does it manually, but this is not what the instructor wants us to do.

Thanks.

2. Hi

The area of the first rectangle is $1 \cdot f\left(\frac12\right)$

The area of the second rectangle is $1 \cdot f\left(1\right)$

and so on

The area of the polygon is $1 \cdot \sum_{k=1}^{4} f\left(\frac{k}{2}\right)$

3. As the base of the rectangles is $\frac{1}{2}$

we need to multiply y by 0.5

However, the answer given is the sum of the areas of the first 5 rectangles.

$\frac{1}{2}\sum_{k=1}^5f\left(k\right)=\frac{1}{2} \left(8+\frac{1}{8}+8+\frac{4}{8}+8+\frac{9}{8}+8+ \frac{16}{8}+8+\frac{25}{8}\right)=\frac{375}{16}= \frac{46.8}{2}$