1. **Problem 1: Find $ \frac{1}{2+6} $ of 54 inches** We are asked to find $ \frac{1}{2+6} $ of 54 inches. 2. **Calculate the denominator:** $$2 + 6 = 8$$ 3. **Rewrite the fraction:** $$\frac{1}{8} \times 54$$ 4. **Multiply:** $$\frac{1}{8} \times 54 = \frac{54}{8}$$ 5. **Simplify the fraction:** $$\frac{54}{8} = \frac{\cancel{54}^{27}}{\cancel{8}^{4}} = \frac{27}{4} = 6.75$$ **Answer:** $6.75$ inches --- 1. **Problem 2: Find the area of the trapezoid with bases 5 cm and 5.4 cm, height 6 cm** The formula for the area of a trapezoid is: $$A = \frac{1}{2} (b_1 + b_2) h$$ where $b_1$ and $b_2$ are the lengths of the two bases, and $h$ is the height. 2. **Plug in the values:** $$A = \frac{1}{2} (5 + 5.4) \times 6$$ 3. **Add the bases:** $$5 + 5.4 = 10.4$$ 4. **Calculate the area:** $$A = \frac{1}{2} \times 10.4 \times 6$$ 5. **Multiply:** $$\frac{1}{2} \times 10.4 = 5.2$$ $$5.2 \times 6 = 31.2$$ **Answer:** $31.2$ square centimeters --- 1. **Problem 3: Find the area of the triangle with base and height given** The formula for the area of a triangle is: $$A = \frac{1}{2} b h$$ 2. **Given values:** base $b = 5.4$ cm, height $h = 2$ cm 3. **Calculate the area:** $$A = \frac{1}{2} \times 5.4 \times 2$$ 4. **Multiply:** $$\frac{1}{2} \times 5.4 = 2.7$$ $$2.7 \times 2 = 5.4$$ **Answer:** $5.4$ square centimeters