Question

The figures below are based on semicircles and squares. Find the perimeter and the area of each shape. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer 1

To find the area, move each semicircle to fill up the square, you'll see there are three squares, each with an area of 4*4=16, so the total area is 3*16=48
Now the perimeter:
the perimeter of a circle is π times the diameter.
perimeter of each semicircle: (1/2)π*4=2π
there are altogether 6 arches and two straight sides, so the total is
2π*6+4*2=12π+8

the area is 48 square units, the perimeter is 12π+8 units.