1. **Problem 1: Find the area of the figure made up of 4 semi-circles and a square with radius 4 mm.** 2. The figure consists of a square and 4 semi-circles attached to each side. The radius of each semi-circle is $4$ mm. 3. The side length of the square equals the diameter of each semi-circle, so side length $s = 2 \times 4 = 8$ mm. 4. Area of the square is given by: $$\text{Area}_{square} = s^2 = 8^2 = 64 \text{ mm}^2$$ 5. Each semi-circle has area: $$\text{Area}_{semi-circle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (4)^2 = 8\pi \text{ mm}^2$$ 6. Total area of 4 semi-circles: $$4 \times 8\pi = 32\pi \text{ mm}^2$$ 7. Total area of the figure is the sum of the square and the 4 semi-circles: $$\text{Area}_{total} = 64 + 32\pi \text{ mm}^2$$ --- 1. **Problem 2: Find the area of the rectangle in the stage hall with base 20 m and height 5 m.** 2. Area of a rectangle is: $$\text{Area} = \text{base} \times \text{height}$$ 3. Substitute values: $$\text{Area} = 20 \times 5 = 100 \text{ m}^2$$ --- 1. **Problem 3: Find the area of the shaded part of a bridge where a semi-circle is cut out from a rectangle. Use $\pi = 3.14$.** 2. Rectangle dimensions: length $= 18$ m, height $= 8$ m. 3. Semi-circle diameter $= 14$ m, radius $r = \frac{14}{2} = 7$ m. 4. Area of rectangle: $$\text{Area}_{rectangle} = 18 \times 8 = 144 \text{ m}^2$$ 5. Area of semi-circle cut out: $$\text{Area}_{semi-circle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 7^2 = \frac{1}{2} \times 3.14 \times 49 = 76.93 \text{ m}^2$$ 6. Area of shaded part (rectangle minus semi-circle): $$\text{Area}_{shaded} = 144 - 76.93 = 67.07 \text{ m}^2$$