Plz help some one
A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π
Is the semicircle inside or outside of the square?
My guess is that it's outside
So if that's the case (which I'm pretty sure it is), find the area of the circle, take half of it, then find the area of the square and add the two together.
Area of circle = pi*r^2 = pi*26^2 = 676pi in^2, then half of it is 338pi
Area of square = s^2 = 26^2 = 676 in^2
So, 338pi in^2 + 676 in^2 = 1737.86 in^2
So the banner has a total area of 1737.86 in^2
To find the total area of the banner, we need to find the area of both the square and the semicircle, and then add them together.
Let's start with the square. The formula to find the area of a square is:
Area of a square = side length x side length
In this case, the side length of the square is 26 inches. So, calculating the area of the square:
Area of the square = 26 inches x 26 inches = 676 square inches
Now, let's move on to the semicircle. The formula to find the area of a semicircle is:
Area of a semicircle = (π x r^2) / 2
In this case, one side of the square also serves as the diameter of the semicircle. So, the radius of the semicircle is half the length of the side of the square, which is 26/2 = 13 inches. Plugging this into the formula:
Area of the semicircle = (3.14 x 13 inches x 13 inches) / 2 = 212.06 square inches
Finally, to find the total area of the banner, we add the area of the square to the area of the semicircle:
Total area of the banner = Area of the square + Area of the semicircle
= 676 square inches + 212.06 square inches
= 888.06 square inches
Therefore, the total area of the banner is approximately 888.06 square inches.