Calculate the PERIMETER of a semicircle

In a new lesson from a Teacher we will see how to calculate the perimeter of a semicircle. First we are going to address the concepts of circumference and perimeter and then define what a semicircle is and how to calculate its perimeter.

Index

1. What is a circle and its elements
2. The perimeter of a circle: formula
3. Calculate the perimeter of a semicircle: formula
4. What is PI = π?
5. Examples to calculate the perimeter of a circle

A circumference is a geometric figure flat and closed shape. Its main characteristic is that all the points that form it are at the same distance from its center. The distance from any point to the center is called the RADIUS.

If we have a fixed point, the center, and a defined distance, we can draw a single circle whose distance will be the radius. By this we mean that a circumference is determined by a center and a radius.

The difference between a circumference and a circle, is that the circle is inside the plane of the circumference, therefore the circumference is the perimeter of the circle.

Elements of a circle

• Center: Point equidistant from all the points that make up the circumference.
• Radio: Segment that joins the center with any of the points of the circumference.
• Diameter: Segment that passing through the center of the circle joins two extreme points of the same. The diameter is therefore twice the radius.
• Rope: Segment that joins any two points on the circle.
• Bow: Curve that joins any two ends of a chord, that is, a portion of the circumference.
• central angles: angle formed by two radii of the circumference.
• Semicircumference: Portion of the circumference that is delimited by two ends of the diameter.

It was determined that the diameter is the largest distance that can be measured between two points that belong to the same circumference.

Here we leave you one classification of geometric solids.

the perimeter, in geometry, means the sum of the lengths of the sides of any plane geometric figure. In mathematics, this is a key concept that is used a lot in conjunction with area and volume. The etymology of the word perimeter comes from ancient Greek and is separated into two parts, on the one hand peri which means "all" and on the other "métron" which means "measure". The first to use the calculation of the perimeter were the Greek philosophers.

This concept is used not only for the length or distance but also the outline of geometric figures. Like the case of the circle that happens to be called circumference. So we can conclude that the perimeter is the length corresponding to the contour of a geometric figure. Therefore, it is the sum of all the sides that make up the figure or in the case of the circle, its circumference.

perimeter of a circle

For calculate the perimeter of a circle We use the radius or the diameter of the circumference and do:

P = 2 x π x r = π x d

• Q: perimeter
• r: radius
• d: diameter

we call semicircumference to each of the equal arcs defined by a diameter. That is, it is a part of the circumference that is delimited by the diameter. We can say that a semicircle is half of a circle.

Taking into account the formula that we saw previously for the perimeter of a complete circle, we are going to Calculate the perimeter of a semicircle.

We again use the number π, the length r and the diameter d to calculate it.

If the perimeter of a circle is

PC = 2 x π x r

And we know that the semicircle is half of the complete circle, we must divide the perimeter into two units, therefore:

Ps = π x r

But here we are missing the line that joins the two ends of the diameter, therefore we have to add 2 x r to the formula

Ps = π x r + 2 x r

semicircle formula

Ps = π x r + 2 x r = r x (2 + π)

The first term of the formula is equal to half the perimeter of a circle of radius r, while the second term is equal to the length of the diameter, or twice the radius.

He PI number, or better known by its symbol 'π', is a irrational number. In mathematics, this means that it is neither exact nor periodic and therefore has an infinite number of decimal places. The number is used as a mathematical constant that is equal to 3.14159…

There are over 12 trillion decimal places of π discovered to date.

This famous number is mainly used or arises to demonstrate lThe ratio between the length of a circle and its diameter.

Let's see some examples to learn how to calculate the perimeter of a circle:

Example 1

Let be a semicircle whose radius is r=3 cm. Get your perimeter.

We calculate

Perimeter = π x r + 2 x r = π x 3 + 2 x 3 = 15.42…. cm

Therefore we obtain as a result that the perimeter of a semicircle of radius 3 cm is 15.42 cm.

Example 2

Calculate the perimeter of a semicircle of radius 6 cm

We calculate

Perimeter = π x r + 2 x r = π x 6 + 2 x 6 = 30.85 cm

The answer is that the perimeter of the semicircle of radius 6 cm is 30.85 cm.

Example 3

Determine the perimeter of a semicircle of radius 10 cm.

We calculate

Perimeter = π x r + 2 x r = π x 10 + 2 x 10 = 51.4 cm

The perimeter is 51.4 cm

If you want to read more articles similar to How to calculate the perimeter of a semicircle, we recommend that you enter our category of Geometry.

• LORENZO, c. g. (2011). CIRCUMFERENCE.
• LORENZO, c. g. Geometric figures.