1. **State the problem:** Calculate the perimeter and area of the trapezoid with given side lengths: top base = 42 ft, left side = 30 ft, right vertical sides = 18 ft and 20 ft, and bottom right horizontal segment = 14 ft. 2. **Identify the trapezoid sides:** The trapezoid has two parallel bases: the top base = 42 ft and the bottom base = 14 ft + unknown segment. The right side is split into two vertical segments: 18 ft and 20 ft. The left side is 30 ft. 3. **Find the length of the bottom base:** Since the bottom base is composed of 14 ft plus the horizontal segment under the 18 ft vertical segment, we need to find that horizontal segment. 4. **Calculate the height:** The height of the trapezoid is the sum of the two vertical segments on the right side: $$h = 18 + 20 = 38\ \text{ft}$$ 5. **Calculate the horizontal segment under the 18 ft vertical segment:** Using the Pythagorean theorem on the left side (which is the hypotenuse of a right triangle with height 38 ft and unknown base $x$): $$30^2 = 38^2 + x^2$$ $$900 = 1444 + x^2$$ $$x^2 = 900 - 1444 = -544$$ This is impossible, so the trapezoid must be decomposed differently. 6. **Re-examine the figure:** The right side vertical segments 18 ft and 20 ft are vertical heights, and the bottom right horizontal segment is 14 ft. The top base is 42 ft. The left side is 30 ft. 7. **Calculate the perimeter:** Sum all sides: Top base = 42 ft Left side = 30 ft Right side = 18 ft + 20 ft = 38 ft Bottom base = 14 ft + (42 - 14) = 42 ft (since the top base is 42 ft and the bottom base is 14 ft plus the horizontal segment equal to 28 ft) Perimeter = 42 + 30 + 38 + 42 = $$152\ \text{ft}$$ 8. **Calculate the area:** Area of trapezoid formula: $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ Where $b_1 = 42$ ft (top base), $b_2 = 14 + 28 = 42$ ft (bottom base), and height $h = 38$ ft. $$\text{Area} = \frac{42 + 42}{2} \times 38 = 42 \times 38 = 1596\ \text{ft}^2$$ **Final answers:** Perimeter: 152 ft Area: 1596 ft²