Find it's circumference and the area
As you see in the picture, it's width is not given but here is what I have tried but can't continue because I have no idea how to find the width of the rectangle.
I started with the circle and found the perimeter and circumference
perimeter: pi*r^2
P: pi*31.5^2 = 3117.24m^2
C: pi*2*31.5= 197.92m
And I do not know how to continue with the rectangle. Or am I even doing this right?
Best Answer
You are dealing with a figure that consists of a rectangle and two semicircles of the same radii. Let $r=31.5$ be the radius of the semicircle and $\ell = 101$ the side of the rectangle.
The perimeter for the figure you have given will be equivalent to adding the sides of the rectangle and half the circumference for both of the semicircles. Since the semicircles have the same radii, you can simply add the two sides of the rectangle and the circumference of the circle with radius $r$.
Thus, the perimeter of your figure is given by $$ 2\ell + 2\pi r = 2(101)+2\pi(31.5) \approx 399.92. $$
For the area: The area will simply be the area of the circle with radius $r$ plus the area of the given rectangle with sides $\ell$ and $2r$. Thus, the area is given by $$ \pi r^2 + \ell\cdot r = \pi(31.5^2)+101\cdot (2\cdot 31.5) \approx 9480.25. $$