Area Calculation: 4×8 Rectangle with Four Semicircles

The area of the entire shape equals the area of the rectangle plus the area of each of the semicircles.

Let's begin by labelling each semicircle with a number:

Therefore, we can determine that:

The area of the entire shape equals the area of the rectangle plus 2A1+2A3

Let's proceed to calculate the area of semicircle A1:

$\frac{1}{2}\pi r^2$

$\frac{1}{2}\pi4^2=8\pi$

Let's now calculate the area of semicircle A3:

$\frac{1}{2}\pi r^2$

$\frac{1}{2}\pi2^2=2\pi$

Therefore the area of the rectangle equals:

$4\times8=32$

Finally we can calculate the total area of the shape:

$32+2\times8\pi+2\times2\pi=32+16\pi+4\pi=32+20\pi$