Ok, let's go for it.
Let x be the side of the square (see picture below).
Let's calculate the perimeter in respect with x.
We know that each semicircle is 15cm.
But ! You know that they are semicircles of a circle which diameter is x.
As the perimeter of a semicircle is half the perimeter of the circle :
Now, the area !
The area is the sum of the areas of :
- the square
- the 4 semicircles.
You should know the area of the square
So let's see what the area of 1 semicircle is :
The area of a semicircle is half the area of the circle.
Hence , where r is actually
So what is the area of the whole thing ?