Final answer:
To calculate the perimeter of the shape, we need to find the sum of the lengths of all the sides. The shape consists of one square and one semicircle. The correct expressions that calculate the perimeter of the shape are D. 12 + 12 + 6.
Step-by-step explanation:
To calculate the perimeter of the shape, we need to find the sum of the lengths of all the sides. The shape consists of one square and one semicircle.
Let's start by finding the perimeter of the square. The formula for the perimeter of a square is P = 4s, where 's' is the length of a side of the square.
Since the square has all sides equal, we can calculate the perimeter of the square by multiplying the length of one side by 4.
Now, let's find the perimeter of the semicircle. The formula for the perimeter of a semicircle is P = πr + 2r, where 'r' is the radius of the semicircle.
Once we calculate the perimeters of both the square and the semicircle, we can add them together to find the total perimeter of the shape.
Let's go step by step to calculate the perimeter:
A:
Perimeter of the square = 4 × length of a side of the square.
B:
Perimeter of the semicircle = π × radius of semicircle + 2 × radius of semicircle.
C:
Total perimeter = Perimeter of the square + Perimeter of the semicircle.
Now, let's calculate the perimeters using the given expressions:
A. 24 + 6:
The expression does not represent the correct calculation for the perimeter of the shape.
B. 36 + 6:
The expression does not represent the correct calculation for the perimeter of the shape.
C. 12 + 24:
The expression does not represent the correct calculation for the perimeter of the shape.
D. 12 + 12 + 6:
This expression represents the correct calculation for the perimeter of the shape. Let's calculate:
A square with one side length of 12 units will have a perimeter of 4 × 12 = 48 units. The semicircle, when stretched to form a full circle, will have a circumference of 2πr = 2 × 12π = 24π units. Adding the perimeter of the square and the semicircle, we get 48 + 24π units. Since the question does not specify the units, we'll keep the answer in terms of units.
E. 12 + 12 + 12 + 6:
The expression does not represent the correct calculation for the perimeter of the shape.
Therefore, the correct expressions that calculate the perimeter of the shape are D. 12 + 12 + 6.