Area of a window. A window is in the shape of a square of side s, with a semicircle of diameter s above it. Write a function that expresses the total area of the window as a function of s.
Well, that's one fancy window design! To calculate the total area, we need to find the area of the square and the area of the semicircle, and then add them together.
The formula for the area of a square is simply s² (side squared). As for the semicircle, we know that the area of a full circle with radius r is πr², so the area of a semicircle is half of that, which means it's (πr²)/2.
In this case, since the diameter of the semicircle is equal to the side of the square, the radius is half the side length, or s/2. So the area of the semicircle is (π(s/2)²)/2.
To get the total area, we just need to add the area of the square and the area of the semicircle. So the function would look like:
```python
def window_area(s):
square_area = s ** 2
semicircle_area = (3.14 * (s/2) ** 2) / 2
total_area = square_area + semicircle_area
return total_area
```
Remember, π is approximately 3.14. So if you want to calculate the area for a specific value of s, you can simply call the function and pass in that value!
To find the total area of the window, we need to calculate the areas of the square and the semi-circle separately, and then add them together.
1. Area of the square:
The area of a square is given by the formula: A = s², where s is the side length of the square.
2. Area of the semi-circle:
The area of a semi-circle is half the area of a full circle with the same diameter. The formula for the area of a circle is: A = πr², where r is the radius. In this case, the diameter of the semi-circle is s, so the radius is half of that, or r = s/2.
Therefore, the area of the semi-circle is: A = (1/2) * π * (s/2)².
3. Total area of the window:
Now, we can add the area of the square and the area of the semi-circle to get the total area of the window:
Total Area = Area of square + Area of semi-circle
= s² + (1/2) * π * (s/2)²
Thus, the function expressing the total area of the window as a function of s is:
f(s) = s² + (1/2) * π * (s/2)²
To calculate the total area of the window, we need to add the area of the square and the area of the semicircle.
The area of a square is found by multiplying the length of one side (s) by itself:
Area of square = s * s = s^2
The area of a semicircle can be calculated by dividing the area of a full circle by 2.
Area of semicircle = (π * (s/2)^2) / 2 = (π * s^2/8)
To find the total area of the window, we add the area of the square and the area of the semicircle:
Total area = Area of square + Area of semicircle
Total area = s^2 + (π * s^2/8)
Therefore, the function expressing the total area of the window as a function of s is:
TotalArea(s) = s^2 + (π * s^2/8)