בכל שרשוט שלפניכם מופיעי ישר החותך שני ישרים מקבילים. מצאו את α:

א. Step 1: Identify the diameter of the semicircles. The semicircles are attached to the sides of the rectangle that measure $20 \text{ cm}$. Therefore, the diameter of each semicircle is $20 \text{ cm}$.

Step 2: Calculate the radius. The radius $r$ is half of the diameter. $r = \frac{diameter}{2} = \frac{20 cm}{2} = 10 \text{ cm}$ The radius of each semicircle is $\boxed{*10 cm*}$.

ב. Step 1: Calculate the area of the rectangle. The dimensions of the rectangle are $40 \text{ cm}$ by $20 \text{ cm}$. $\text{Area of rectangle} = length \times width = 40 cm \times 20 cm = 800 cm^2$

Step 2: Calculate the area of the two semicircles. Two identical semicircles form one full circle. The radius of this circle is $10 \text{ cm}$ (from part a). $\text{Area of circle} = \pi r^2 = \pi (10 cm)^2 = 100\pi cm^2$

Step 3: Calculate the total area of the shape. The total area is the sum of the area of the rectangle and the area of the two semicircles. $\text{Total Area} = 800 cm^2 + 100\pi cm^2 \approx 800 + 100(3.14159) cm^2 \approx 800 + 314.159 cm^2 \approx 1114.16 cm^2$ The total area of the shape is $\boxed{*(800 + 100\pi) cm^2 \approx 1114.16 cm^2*}$.

ג. Step 1: Identify the segments that form the perimeter. The perimeter consists of the two longer sides of the rectangle and the arc lengths of the two semicircles. The dashed segment is not part of the perimeter.

Step 2: Calculate the length of the two longer sides of the rectangle. Each longer side is $40 \text{ cm}$. $\text{Length of two sides} = 2 \times 40 cm = 80 \text{ cm}$

Step 3: Calculate the total arc length of the two semicircles. The arc length of two identical semicircles is equal to the circumference of one full circle with radius $10 \text{ cm}$. $\text{Circumference of circle} = 2\pi r = 2\pi (10 cm) = 20\pi \text{ cm}$

Step 4: Calculate the total perimeter of the shape. The total perimeter is the sum of the lengths calculated in Step 2 and Step 3. $\text{Total Perimeter} = 80 cm + 20\pi cm \approx 80 + 20(3.14159) cm \approx 80 + 62.8318 cm \approx 142.83 \text{ cm}$ The perimeter of the shape is $\boxed{*(80 + 20\pi) cm \approx 142.83 cm*}$.