The perimeter of a semi-circle uses a different formula compared to that of the full circle. As the name implies, the semi-circle is half of a complete Circle. Also, finding its perimeter simply comprises discovering its diameter and adding it to the half the perimeter of a complete circle.
Students are often required to complete the perimeter of a semi-circle, and there is often the belief that it’s a quite tasking computation. However, this claim is in no way close to reality, as the circle’s perimeter is as simple as computing a circle perimeter. Like the circle, all that must be available in the semi-circle radius.
This article will highlight a comprehensive and easy way to compute the semi-circle perimeter with examples.
The Semi-circle
The semi-circle is the half of the circle separated in the middle, which is the diameter. As such, the semi-circle is all around is half a circumference and a diameter.
Below are a circle and a semi-circle.
As evident above, while the circle is a complete round arc, the semi-circle is half an arc and a diameter. It is based on these definitions will the perimeter of the semi-circle be found.
The Perimeter of a Semicircle Formula
The perimeter of a semi-circle is the addition of the diameter and half the circumference of a complete circle.
It is mathematically given as
P = D + πr
Where D = the diameter of the semi-circle and two times the radius
r = radius, which is often half the diameter
π = a constant equal to 3.142
The formula for the perimeter of the circle is derived from that of the full circle.
The perimeter of a complete circle is the same as the circumference of the circle and is given as
P = 2πr
Since the perimeter or circumference of the circle is 2πr, and the semi-circle is actually half circumference and diameter, then it will only make sense for the latter to be expressed
Diameter + half of a circumference
That will therefore be
P = D + ½ x 2πr
P = D + πr
The above is how the formula for the semi-circle is gotten.
How to Calculate the Perimeter of a Semi-circle?
Below are the steps to calculate the perimeter of the circle
Step 1: write down the formula
Step 2: input the diameter or radius into the formula and start your computation.
Examples that highlight how to calculate the Semi-circle
Example 1
Find the perimeter of a semi-circle with a 14 cm radius
Solution
We will use the steps outlined in this article to find the perimeter
Step 1: write down the formula
P = D + πr
Where r = radius, π = 3.142, D = 2r
Step 2: input the diameter or radius into the formula and start your computation.
Since r = 14 cm, D = 2 x 14 cm = 28 cm
Therefore;
P = 28 + 3.142 x 14
P = 28 + 43.99
P = 71.99
Example 2
Let the diameter of a semi-circle be 31 cm, and find its perimeter?
Solution
The same method that we used in solving the first example will also be applied to solve this one. However, the only difference in this case is that the diameter was given instead of the radius. However, that is not the problem, as the diameter only needs to be divided to find the radius.
The formula for the perimeter of the semicircle is given as;
P = D + πr
Where D = 31 cm,
π = 3.142 cm,
r = 31cm/2 = 15.5 cm.
P = 31 cm + 3.142 x 15.5 cm
P = 79.701 cm
Example 3
Consider a semi-circle whose perimeter is given as 48 cm. determine its radius.
Solution
Since the perimeter has already been given, we can find the radius of the circle the same way
P = D + πr
48 cm = D + 3.142r, since π = 3.142
Also since D = 2r,
48 cm = 2r + 3.142r
48 cm = 5.142r
48/5.142 = r
9.335 cm = r
Therefore the radius of the semi-circle is 9.335 cm.
Conclusion
The perimeter of a semi-circle is a branch of the entire computation about the circle and its circumference. The Semi-circle perimeter, as expected, has its formula carved out from that of the circle. As shown in this article, calculating it is just as easy as that of the circle.
In this article, comprehensive calculations of the semi-circle were carried out with all steps systematically outlined. Three examples were also considered to show students possible questions they may have to deal with in class, tests or exams. The formula and manipulations highlighted in this article can be trusted to help students go about their respective calculations.
