Answer:
Circumference: 12π + 8 cm,
Area: 48 ( cm )^2
Step-by-step explanation:
This figure is composed of circles, squares, and semicircles. As you can see, the squares indicate that each semicircle should have ( 1 ) the same area, and ( 2 ) the same length ( circumference ). It would be easier to take the circumference of the figure first, as it is composed of arcs part of semicircles the same length.
Circumference of 1 semicircle = [tex]\frac{1}{2}[/tex]( πd ) = [tex]\frac{1}{2}[/tex]π( 4 ) = 2π ( cm )
Circumference of Figure (composed of 6 semicircles + 2 sides of a square),
We know that 6 semicircles should be 6 [tex]*[/tex] 2π, and as the sides of a square are equal - if one side is 4 cm, the other 3 are 4 cm as well. Therefore the " 2 sides of a square " should be 2
Circumference of Figure = 6 [tex]*[/tex] 2π + 2 = 12π + 8 ( cm )
_____________
The area of this figure is our next target. As you can see, it is composed of 3 semicircles, and the area of 3 semicircles subtracted from the area of 3 squares. Therefore, let us calculate the area of 1 semicircle, and the area of 1 square first.
Area of 1 semicircle = 1/2π[tex]r^2[/tex] = 1/2π[tex](2)^2[/tex] = 2π ( cm ),
Area of 1 square = ( 4 cm )( 4 cm ) = 16 ( [tex]cm^2[/tex] )
So, the area of the figure should be the following -
Area of Figure = 3 [tex]*[/tex] 2π + 3( 16 - 2π ) = 48 ( cm )^2
