Question

A composite figure is comprised of a square and 4 semicircles.
How can you decompose the composite figure to determine its area?

as a pentagon and four semicircles
as two rectangles and four circles
as a square and four semicircles
as two triangles and four circles

Answer 1

As a square and four semicircles.

Reason: the figure is literally a square plus four semicircles, so
Area = area(square) + area(4 semicircles)
= s^2 + 4*(1/2)πr^2 = s^2 + 2πr^2.

If each semicircle has diameter equal to the square side s (so r = s/2), then
Area = s^2 + 2π(s/2)^2 = s^2 + (π/2)s^2 = s^2(1 + π/2).