the perimeter of a semicircular region is 20. find the area of the region
To find the area of a semicircular region, we need to know the radius of the semicircle.
Let's denote the radius as 'r'.
First, let's find the circumference (perimeter) of the semicircular region. The formula for the circumference of a full circle is C = 2πr. Since we only have a semicircle, the circumference of the semicircular region will be half of the circumference of a full circle. Therefore, the circumference of the semicircular region is C = πr.
We are given that the circumference is 20. So we can write the equation as:
πr = 20.
To find the radius, divide both sides of the equation by π:
r = 20/π.
Now that we know the radius, we can find the area of the semicircular region. The formula for the area of a semicircle is A = (πr^2)/2.
Substituting the value of the radius:
A = (π*(20/π)^2)/2 = (400/π)/2 = 200/π.
Hence, the area of the semicircular region is 200/π (or approximately 63.66 if you prefer a decimal approximation).