1. **Problem statement:** Find the area of each trapezoid given the bases and height. 2. **Formula for the area of a trapezoid:** $$A = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two parallel bases, and $h$ is the height. --- ### a) Trapezoid with bases 4 cm and 10 cm, height 6 cm 3. Substitute values into the formula: $$A = \frac{(4 + 10)}{2} \times 6$$ 4. Simplify inside the parentheses: $$A = \frac{14}{2} \times 6$$ 5. Cancel common factor 2 in denominator and numerator: $$A = \cancel{\frac{14}{2}} \times 6 = 7 \times 6$$ 6. Multiply: $$A = 42$$ 7. **Answer:** The area of trapezoid a is $42$ cm$^2$. --- ### b) Trapezoid with bases 8 cm and 8 cm, height 10 cm 8. Substitute values: $$A = \frac{(8 + 8)}{2} \times 10$$ 9. Simplify inside parentheses: $$A = \frac{16}{2} \times 10$$ 10. Cancel common factor 2: $$A = \cancel{\frac{16}{2}} \times 10 = 8 \times 10$$ 11. Multiply: $$A = 80$$ 12. **Answer:** The area of trapezoid b is $80$ cm$^2$. --- ### c) Trapezoid with bases 10 cm and 20 cm, height 6 cm 13. Substitute values: $$A = \frac{(10 + 20)}{2} \times 6$$ 14. Simplify inside parentheses: $$A = \frac{30}{2} \times 6$$ 15. Cancel common factor 2: $$A = \cancel{\frac{30}{2}} \times 6 = 15 \times 6$$ 16. Multiply: $$A = 90$$ 17. **Answer:** The area of trapezoid c is $90$ cm$^2$. --- **Summary:** - Area a = 42 cm$^2$ - Area b = 80 cm$^2$ - Area c = 90 cm$^2$