The perimeter of a semi-circle is the sum of the length of its curved edge and the diameter of the semi-circle. The formula for the perimeter of a semi-circle is:

Perimeter of Semi-Circle = πr + 2r = r(π+2)

Where r is the radius of the semi-circle and π (pi) is a mathematical constant approximately equal to 3.14.



The area of a circle is the amount of space enclosed by the circle. The formula for the area of a circle is:

Area of Circle = πr²

Where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

To understand this formula, let's imagine a circle with radius r. We can divide the circle into small sectors or pieces, each with an angle of θ. The area of each sector is approximately equal to the area of a triangle with base r and height (r x sin(θ/2)). The total area of the circle is the sum of all these sectors. As the number of sectors increases, the approximation becomes more accurate, and we get the exact formula for the area of a circle:

Area of Circle = lim(n→∞) [n x r² x sin(360/n) / 2]

Where n is the number of sectors, and the limit (as n approaches infinity) ensures that we get the exact area of the circle.

In conclusion, the area of a circle is a fundamental concept in geometry and has many real-world applications. It is calculated using the formula πr², where r is the radius of the circle. The formula for the perimeter of a semi-circle is r(π+2), where r is the radius of the semi-circle.

Perimeter of semicircle = 1/2(pie × d)+d. d is a diameter of semi circle....