To solve this problem, we need to follow a step-by-step approach. Given that we have a square and two equilateral triangles sharing two sides of this square, we will calculate the perimeter of the compound shape in centimeters first, and then convert it into millimeters.
1. Identify the side length of the square and the triangles:
One side of the square measures 3 cm. Each equilateral triangle also has sides that measure 3 cm since they sit on the sides of the square.
2. Calculate the perimeter contributed by the square:
- The square has 4 sides.
- Each side of the square is 3 cm.
- So, the total perimeter contributed by the square is [tex]\( 4 \times 3 = 12 \)[/tex] cm.
3. Calculate the perimeter contributed by the triangles:
- Each equilateral triangle has 3 sides.
- Since there are two triangles, the total amount of triangle sides is [tex]\( 3 \times 2 = 6 \)[/tex] sides.
- Each side of both equilateral triangles measures 3 cm.
- Thus, the perimeter contributed by the triangles is [tex]\( 6 \times 3 = 18 \)[/tex] cm.
4. Sum the perimeters to get the total perimeter in centimeters:
- Total perimeter [tex]\( = \text{perimeter of the square} + \text{perimeter of the triangles} \)[/tex].
- Total perimeter [tex]\( = 12 \, \text{cm} + 18 \, \text{cm} = 30 \, \text{cm} \)[/tex].
5. Convert the total perimeter from centimeters to millimeters:
- There are 10 millimeters in 1 centimeter.
- Therefore, multiply the total perimeter by 10 to get it in millimeters.
- [tex]\( 30 \, \text{cm} \times 10 = 300 \, \text{mm} \)[/tex].
So, the perimeter of the compound shape in millimeters is 300 mm. Therefore, the correct answer is:
C. 300 mm
