1. **State the problem:** We have a square with side length 4.5 cm. An equilateral triangle with side length 4.5 cm is cut out from one side of the square, creating a "V" shape inset. We need to find the perimeter of the resulting shape. 2. **Understand the shape:** The original square has 4 equal sides of 4.5 cm each. 3. **Effect of cutting out the equilateral triangle:** The triangle is cut out from one side of the square, replacing that side with two sides of the triangle (each 4.5 cm) meeting at a point inside the square. 4. **Calculate the new perimeter:** - The three sides of the square remain, each 4.5 cm, so total length from these is $$3 \times 4.5 = 13.5$$ cm. - The top side of the square (4.5 cm) is replaced by two sides of the equilateral triangle, each 4.5 cm, so total length from these two sides is $$2 \times 4.5 = 9$$ cm. 5. **Sum the perimeter:** $$\text{Perimeter} = 13.5 + 9 = 22.5$$ cm. **Final answer:** The perimeter of the shape after cutting out the equilateral triangle is **22.5 cm**.