1. **Problem Statement:** Calculate the area of each triangle and trapezoid given their dimensions. 2. **Formula for Area of Triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ The base and height must be perpendicular. 3. **Formula for Area of Trapezoid:** $$\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$$ The bases are the two parallel sides. --- ### Triangles: **N)** Base = 12 mm, Height = 11 mm $$\text{Area}_N = \frac{1}{2} \times 12 \times 11 = 6 \times 11 = 66 \text{ mm}^2$$ **M)** Base = 6 cm, Height = 4 cm $$\text{Area}_M = \frac{1}{2} \times 6 \times 4 = 3 \times 4 = 12 \text{ cm}^2$$ **A)** Base = 9 ft, Height = 6 ft $$\text{Area}_A = \frac{1}{2} \times 9 \times 6 = 4.5 \times 6 = 27 \text{ ft}^2$$ **H)** Base = 12 in, Height = 7 in $$\text{Area}_H = \frac{1}{2} \times 12 \times 7 = 6 \times 7 = 42 \text{ in}^2$$ **S)** Base = 4 m, Height = 8 m $$\text{Area}_S = \frac{1}{2} \times 4 \times 8 = 2 \times 8 = 16 \text{ m}^2$$ **V)** Base = 4 m, Height = 4 m $$\text{Area}_V = \frac{1}{2} \times 4 \times 4 = 2 \times 4 = 8 \text{ m}^2$$ --- ### Trapezoids: **1)** Bases = 5 in, 4 in; Height = 6 in $$\text{Area}_1 = \frac{1}{2} \times (5 + 4) \times 6 = \frac{1}{2} \times 9 \times 6 = 27 \text{ in}^2$$ **2)** Bases = 5 mm, 8 mm; Height = 6 mm $$\text{Area}_2 = \frac{1}{2} \times (5 + 8) \times 6 = \frac{1}{2} \times 13 \times 6 = 39 \text{ mm}^2$$ **3)** Bases = 7 m, 5 m; Height = 2 m $$\text{Area}_3 = \frac{1}{2} \times (7 + 5) \times 2 = \frac{1}{2} \times 12 \times 2 = 12 \text{ m}^2$$ **4)** Bases = 7 yd, 1 yd; Height = 9 yd $$\text{Area}_4 = \frac{1}{2} \times (7 + 1) \times 9 = \frac{1}{2} \times 8 \times 9 = 36 \text{ yd}^2$$ **5)** Bases = 6 cm, 4 cm; Height = 3 cm $$\text{Area}_5 = \frac{1}{2} \times (6 + 4) \times 3 = \frac{1}{2} \times 10 \times 3 = 15 \text{ cm}^2$$ **6)** Bases = 4 ft, 5 ft; Height = 2 ft $$\text{Area}_6 = \frac{1}{2} \times (4 + 5) \times 2 = \frac{1}{2} \times 9 \times 2 = 9 \text{ ft}^2$$ --- ### Decoder Box and Code Word: From the decoder box: - 27 → L - 20 → G - 14 → T - 25 → R - 26 → I - 21 → E - 12 → D - 28 → S - 35 → G - 22 → O - 18 → U - 30 → A Using the triangle areas and trapezoid areas to find letters: Triangles: - N = 66 (not in decoder) - M = 12 → D - A = 27 → L - H = 42 (not in decoder) - S = 16 (not in decoder) - V = 8 (not in decoder) Trapezoids: - 1 = 27 → L - 2 = 39 (not in decoder) - 3 = 12 → D - 4 = 36 (not in decoder) - 5 = 15 (not in decoder) - 6 = 9 (not in decoder) Final code word letters from known values: M = D, A = L, 1 = L, 3 = D --- **Final answers:** - Area of triangle N: $66$ mm² - Area of triangle M: $12$ cm² - Area of triangle A: $27$ ft² - Area of triangle H: $42$ in² - Area of triangle S: $16$ m² - Area of triangle V: $8$ m² - Area of trapezoid 1: $27$ in² - Area of trapezoid 2: $39$ mm² - Area of trapezoid 3: $12$ m² - Area of trapezoid 4: $36$ yd² - Area of trapezoid 5: $15$ cm² - Area of trapezoid 6: $9$ ft² Code letters from decoder box for areas 12 and 27 are D and L respectively.