Answer:
The Perimeter figure is: 21.42 mm
Explanation:
The given figure consists of two parts:
1) Semicircle
2) Square
Determining the Perimeter of the Semicircle:
Given
Diameter d = 6 mm
Radius r = d/2 = 6/2 = 3 mm
In a semi-circle, the perimeter is made up of half the circumference (arc) of the circle and the diameter of the circle.
Perimeter = 1/2 × ( circumference of the circle ) + d
= 1/2 × (2πr) + d
= πr + d
= 3.14(3) + 6
= 9.42 + 6
= 15.42 mm
Thus, the Perimeter of the semi-circle is: 15.42 mm
Determining the Perimeter of the Square:
Given
Length of a side = a = 2mm
Perimeter of square = 4a = 4(2) = 8mm
Thus, the Perimeter of the Square is: 8mm
Now, in order to determine the Perimeter of a complete figure, we need to add the Perimeter of the square and the perimeter of the semicircle and subtract 2 mm.
The reason why we need to subtract 2mm because one side of the square (2mm) is overlapped along the diameter of the semicircle.
Now,
Figure Perimeter = Perimeter of square + Perimeter of Semicircle - 2
= 8 + 15.42 - 2
= 21.42 mm
Therefore, the Perimeter figure is: 21.42 mm
Note: It seems you may have missed adding the correct choice there.