1. **Problem 1: Find the area of the shaded section inside the large circle with two smaller circles stacked vertically.** 2. The large circle contains two smaller circles stacked vertically, each with radius 3.00 cm. 3. The area of a circle is given by the formula $$A = \pi r^2$$ where $r$ is the radius. 4. Calculate the area of the large circle. Since the two smaller circles are stacked vertically and each has radius 3.00 cm, the diameter of each small circle is $2 \times 3 = 6$ cm. The large circle must have radius equal to the sum of the two small circles' diameters divided by 2, so radius of large circle is $r = 6$ cm. 5. Area of large circle: $$A_{large} = \pi \times 6^2 = 36\pi$$ 6. Area of one small circle: $$A_{small} = \pi \times 3^2 = 9\pi$$ 7. Total area of two small circles: $$2 \times 9\pi = 18\pi$$ 8. Area of shaded section (large circle minus two small circles): $$A_{shaded} = 36\pi - 18\pi = 18\pi$$ 9. **Problem 2: Find the perimeter and area of the composite figure made of an 8 cm by 5 cm rectangle and a right triangle attached to the right side, with total bottom length 14 cm.** 10. The rectangle has width 8 cm and height 5 cm. 11. The right triangle is attached to the right side of the rectangle, so the base of the triangle is $14 - 8 = 6$ cm. 12. The height of the triangle is the same as the rectangle's height, 5 cm. 13. Area of rectangle: $$A_{rect} = 8 \times 5 = 40$$ 14. Area of triangle: $$A_{tri} = \frac{1}{2} \times 6 \times 5 = 15$$ 15. Total area: $$A_{total} = 40 + 15 = 55$$ 16. Perimeter calculation: - Left side of rectangle: 5 cm - Top side of rectangle: 8 cm - Hypotenuse of triangle: $$\sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61}$$ - Right side of triangle: 5 cm - Bottom side: 14 cm 17. Total perimeter: $$P = 5 + 8 + \sqrt{61} + 5 + 14 = 32 + \sqrt{61}$$ 18. Approximate numeric value: $$\sqrt{61} \approx 7.81$$ $$P \approx 32 + 7.81 = 39.81$$ **Final answers:** - Area of shaded section: $$18\pi \approx 56.55$$ - Area of composite figure: 55 - Perimeter of composite figure: approximately 39.81