Question

Find the area of this compound shape. How to solve this?

Answer 1

Check the picture below.

so we're looking for the shaded section with the semi-circles, so hmm notice, the semi-circle on the left if added to the one on the right, make up a full circle with a diameter of 5 or a radius of half that or 2.5 cm, and the semi-circle atop is just a semi-circle with a diameter of 4 or namely a radius of half that or 2 cm.

The containing shape is really just a 6x9 rectangle as you can see in the shade, so let's just get the area of that rectangle and then subtract the areas of the full circle and the semi-circle atop, what's leftover is what we didn't subtract, the area of the shape.

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{ rectangle }{(6)(9)}~~ - ~~\stackrel{ \textit{full circle} }{\pi (2.5)^2}~~ - ~~\stackrel{ semi-circle }{\cfrac{1}{2}\pi (2)^2}}\implies 54~~ - ~~6.25\pi ~~ - ~~2\pi \\\\\\ 54-4.25\pi ~ \approx ~ \text{\LARGE 40.6}~cm^2`