I have a picture of a window showing a square in the center with sides measuring 4 feet, over each side of the square is a semi-circle(a total of 4 semi-circles), how can I find the area of the window? Should I find the area of the square and the semi-circles and add them together?
so the semicircles have a radius of 2 feet, and the 4 semicircles would be the same as 2 complete circles.
total area = square + 2 circles
= 16 + 2(π(2^2)) = 16 + 8π
Yes, to find the area of the window, you should first find the area of the square and then add the areas of the four semi-circles. Here's how you can calculate it step-by-step:
1. Find the area of the square:
The area of a square is calculated by multiplying the length of one side by itself. Since each side of the square measures 4 feet, the area of the square is 4 feet * 4 feet = 16 square feet.
2. Find the area of one semi-circle:
The formula to calculate the area of a semi-circle is (π * r^2) / 2, where π (pi) is a mathematical constant approximately equal to 3.14159 and r is the radius of the semi-circle.
Since the semi-circle is formed by the top side of the square, its radius is half the length of the side of the square, which is 4 feet. Therefore, the area of one semi-circle is (3.14159 * 4^2) / 2 = 25.132 square feet.
3. Calculate the total area of the four semi-circles:
Multiply the area of one semi-circle (25.132 square feet) by 4, which gives you a total area of 100.528 square feet.
4. Add the area of the square and the total area of the four semi-circles:
Add the area of the square (16 square feet) to the total area of the four semi-circles (100.528 square feet) to get the final area of the window:
16 square feet + 100.528 square feet = 116.528 square feet.
Therefore, the area of the window is approximately 116.528 square feet.