Question

1. find the perimeter of the complex figure below. show your work neatly, organize. (perimeter is all sides added together) 2.5 cm 12.3cm 9.3cm 3 cm 3 cm 5.5cm

Explanation:

Answer:

To find the perimeter, we can use the method of "translating" the horizontal and vertical segments to form a rectangle (since the horizontal "indent" can be moved right and the vertical "indent" can be moved up, making the figure equivalent to a rectangle in terms of perimeter).

First, find the length and width of the equivalent rectangle:

• Length: \( 12.3 \, \text{cm} \) (vertical side)
• Width: \( 5.5 \, \text{cm} \) (horizontal side)

The perimeter of a rectangle is given by \( P = 2 \times (\text{length} + \text{width}) \).

Substitute the values:
\( P = 2 \times (12.3 + 5.5) \)
\( P = 2 \times 17.8 \)
\( P = 35.6 \, \text{cm} \)

(Alternatively, by adding all sides:
Top: \( 2.5 + 3 = 5.5 \, \text{cm} \)
Right: \( 9.3 + 3 = 12.3 \, \text{cm} \)
Bottom: \( 5.5 \, \text{cm} \)
Left: \( 12.3 \, \text{cm} \)
Perimeter: \( 5.5 + 12.3 + 5.5 + 12.3 = 35.6 \, \text{cm} \))

Final answer: \( \boldsymbol{35.6 \, \text{cm}} \)