The area of the composite figure with 3 semicircles connected to 3 sides of a square is (6π+16)[tex]cm^{2}[/tex].
What is a semicircle?
A semicircle is a plane shape that is a part of a circle divided into two equal parts through its diameter.
Analysis:
Since the semicircles are connected to 3 sides of a square 4cm, the diameter of the semicircle is 4cm.
Radius of semicircle = 4/2 = 2cm
Area of a semicircle = π[tex]r^{2}[/tex]/2 = [tex]\pi[/tex][tex](2)^{2}[/tex]/2 = 2π[tex]cm^{2}[/tex]
For three semicircles = 3 x 2π[tex]cm^{2}[/tex] = 6π[tex]cm^{2}[/tex]
Area of square = [tex]s^{2}[/tex] = [tex](4)^{2}[/tex] = 16[tex]cm^{2}[/tex]
Area of composite figure = Area of 3 semicircles + area of square
Area of composite figure = (16 + 6π)[tex]cm^{2}[/tex]
In conclusion, the area of the composite figure is (16 + 6π)[tex]cm^{2}[/tex].
Learn more about area of plane shapes: brainly.com/question/20475473
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