Area Stair Step 5Cf8E0

1. **State the problem:** We have a figure made of six identical squares arranged in a stair-step pattern. The total perimeter of the figure is $56$ cm. We need to find the area of the figure in $cm^2$. 2. **Analyze the figure and variables:** Let the side length of each square be $s$ cm. 3. **Count the squares:** There are $6$ identical squares. 4. **Calculate the perimeter:** The perimeter is the total length around the figure. Because the squares are arranged in a stair-step pattern, some sides are shared and do not contribute to the perimeter. 5. **Determine the perimeter in terms of $s$:** The figure has $6$ squares arranged as follows: - Top row: 1 square - Second row: 2 squares - Third row: 2 squares - Bottom row: 1 square The perimeter consists of the outer edges only. 6. **Calculate the total perimeter in terms of $s$:** The figure's perimeter is $14s$ because the shape has 14 outer edges of length $s$ (counting carefully the stair-step shape). 7. **Set up the equation:** $$14s = 56$$ 8. **Solve for $s$:** $$s = \frac{56}{14} = 4$$ 9. **Calculate the area:** The area of one square is: $$s^2 = 4^2 = 16$$ Since there are 6 squares, total area is: $$6 \times 16 = 96$$ 10. **Final answer:** The area of the figure is $96$ $cm^2$.