1. **State the problem:** Find the area of each given shape. 2. **Formulas and rules:** - Square area: $A = s^2$ where $s$ is the side length. - Trapezoid area: $A = \frac{1}{2}(b_1 + b_2)h$ where $b_1, b_2$ are parallel sides and $h$ is height. - Rectangle area: $A = lw$ where $l$ is length and $w$ is width. - Right triangle area: $A = \frac{1}{2}bh$ where $b$ is base and $h$ is height. 3. **Calculate each area:** **i. Square with side 4 cm:** $$A = 4^2 = 16\text{ cm}^2$$ **ii. Trapezoid with bases 8 cm and 15 cm, height 6 cm:** $$A = \frac{1}{2}(8 + 15) \times 6 = \frac{1}{2} \times 23 \times 6$$ $$= \cancel{\frac{1}{2}} \times 23 \times \cancel{6}^3 = 23 \times 3 = 69\text{ cm}^2$$ **iii. Rectangle with length 15 cm and width 6 cm:** $$A = 15 \times 6 = 90\text{ cm}^2$$ **iv. Right triangle with base 8 cm and height 12 cm:** $$A = \frac{1}{2} \times 8 \times 12 = \frac{1}{2} \times \cancel{8}^4 \times \cancel{12}^6 = 4 \times 6 = 24\text{ cm}^2$$ 4. **Final answers:** - Square area = 16 cm² - Trapezoid area = 69 cm² - Rectangle area = 90 cm² - Right triangle area = 24 cm² Each area is calculated using the appropriate formula and simplified step-by-step for clarity.