How to Calculate the Perimeter of a Semi-circle?

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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.

the circle the 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.

How to Calculate the Perimeter of a Semi-circle?

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