1. **State the problem:** We need to find the perimeter and area of a polygon composed of a rectangle and a right triangle attached to its right side. 2. **Identify given dimensions:** - Rectangle height = 15 ft - Rectangle base = 18 ft - Triangle base (top side) = 8 ft - Triangle hypotenuse (right slanted side) = 17 ft 3. **Find the missing side of the triangle:** Since the triangle is right-angled, use the Pythagorean theorem: $$\text{hypotenuse}^2 = \text{base}^2 + \text{height}^2$$ Let the triangle height be $h$: $$17^2 = 8^2 + h^2$$ $$289 = 64 + h^2$$ $$h^2 = 289 - 64 = 225$$ $$h = \sqrt{225} = 15 \text{ ft}$$ 4. **Calculate the area:** - Area of rectangle: $$A_{rect} = \text{base} \times \text{height} = 18 \times 15 = 270 \text{ sq ft}$$ - Area of triangle: $$A_{tri} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 15 = 60 \text{ sq ft}$$ - Total area: $$A = A_{rect} + A_{tri} = 270 + 60 = 330 \text{ sq ft}$$ 5. **Calculate the perimeter:** The perimeter includes: - Left side of rectangle = 15 ft - Bottom side of rectangle = 18 ft - Top side of rectangle plus triangle base = 18 + 8 = 26 ft - Hypotenuse of triangle = 17 ft - Right vertical side of triangle = 15 ft However, the right vertical side of the triangle coincides with the rectangle's right side, so it is counted once. Perimeter $P$ is: $$P = 15 + 18 + 17 + 15 + 8 = 73 \text{ ft}$$ But note the top side is 18 + 8 = 26 ft, so the perimeter is: $$P = 15 + 18 + 17 + 15 + 8 = 73 \text{ ft}$$ Re-examining the perimeter sides: - Left side (rectangle): 15 ft - Bottom side (rectangle): 18 ft - Triangle hypotenuse: 17 ft - Triangle base (top side): 8 ft - Top side of rectangle: 18 ft But the top side of rectangle and triangle base are adjacent, so the top side is 18 + 8 = 26 ft total. The perimeter is the sum of: - Left side: 15 ft - Bottom side: 18 ft - Hypotenuse: 17 ft - Top side: 26 ft So: $$P = 15 + 18 + 17 + 26 = 76 \text{ ft}$$ **Final answers:** - Perimeter $P = 76$ feet - Area $A = 330$ square feet