1. **Problem Statement:** Find the perimeter and area of the given shape, which is a right triangle with a smaller square inside it at the bottom-left corner. 2. **Understanding the shape:** The large right triangle has legs of 4 in (vertical) and 3 in (horizontal), and the hypotenuse is 5 in. Inside it, there is a square of side 3 in at the bottom-left corner. 3. **Perimeter of the shape:** The perimeter of the shape is the sum of the outer sides of the large triangle since the square is inside and does not add to the outer perimeter. 4. **Calculate the perimeter:** The triangle sides are 3 in, 4 in, and 5 in. $$\text{Perimeter} = 3 + 4 + 5 = 12$$ 5. **Area of the triangle:** The area of a right triangle is given by $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ Here, base = 3 in and height = 4 in. 6. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 3 \times 4 = \frac{12}{2} = 6$$ 7. **Area of the square:** The square has side length 3 in, so $$\text{Area}_{square} = 3 \times 3 = 9$$ 8. **Total area of the shape:** Since the square is inside the triangle, the total area of the shape is the area of the triangle minus the area of the square. $$\text{Total Area} = 6 - 9 = -3$$ This negative value indicates the square cannot be inside the triangle as described with these dimensions; likely the square is part of the shape, so the problem likely asks for the triangle's perimeter and area only. **Final answers:** - Perimeter = 12 in - Area = 6 square inches