Hey, I'm confused on this one problem and can you help me please? Thanks a bunch! :]
The problem is:
The figure consists of a square with 4 half circles surrounding it. If the perimeter of the figure is 87 yards, what is the radius of each half circle? What is the area of the square? Round to the nearest tenth if necessary.
THANKS XD
A square has 4 equal sides, so 87/4 will give you the length of one side, which happens to be 21.75 yards. Not only is this the length of a side of a square, but it is also the diameter of the half circle. Do 21.75/2 to get the radius, which comes out to be 10.875 yards. As for the area of the square, just square the length of a side. 21.75^2 = 473.0625 yards.
So your final answers:
r = 10.875 yards
A = 473.0625 yards
Round however you'd like.
Of course, I'd be happy to help you with that problem! To find the radius of each half circle, we need to first find the total circumference of all four half circles combined.
Let's start by finding the perimeter of the figure. The figure consists of a square and four half circles. The perimeter of the square is equal to the sum of all four sides. Since all the sides of the square are equal in length, we can find the perimeter of the square by multiplying the length of one side by 4.
Let's assume that each side of the square has a length of "s" yards. Therefore, the perimeter of the square would be 4s yards.
We also know that the total perimeter of the figure is given as 87 yards. Therefore, we can set up an equation:
Perimeter of square + Total circumference of half circles = Total Perimeter
4s + Total circumference of half circles = 87
Now, let's find the circumference of one half circle. The circumference of a circle is given by the formula: C = 2 * π * r, where "C" represents the circumference and "r" represents the radius of the circle.
Since each half circle has a radius, we can find the circumference of one half circle by substituting the given values into the formula:
Circumference of one half circle = 2 * π * r
Now, since there are four half circles surrounding the square, the total circumference of all four half circles combined would be 4 times the circumference of one half circle.
Total circumference of half circles = 4 * (2 * π * r) = 8 * π * r
Now, substitute this value in the equation to solve for "r":
4s + 8 * π * r = 87
To find the radius, we need to solve for "r" in this equation.
Now, let's move on to finding the area of the square. The area of a square can be calculated by multiplying the length of one side by itself. In this case, the side of the square is "s".
Therefore, the area of the square would be:
Area of square = s * s = s^2
You can calculate the area by substituting the value of "s" into the formula.
Once you have solved the equation to find the value of "r", you can then substitute the value into the formula to find the area of the square.
I hope this explanation helps you understand how to approach and solve the problem. Let me know if you have any further questions!