Semicircle - Shape, Definition, Properties, Examples - Cuemath

Semicircle

A semicircle is one of the most common shapes seen in geometry in the form of a protractor. A semicircle is half of a circle and some of the real-life examples that we see around us are a railway tunnel through which a train passes by, an igloo, half a watermelon, and much more. All these shapes resemble a semi-circle while drawn on a 2D plane.

1.	What is Semicircle?
2.	Area of a Semicircle
3.	Circumference of a Semicircle
4.	Semicircle Perimeter
5.	Angle Inscribed in a Semicircle
6.	FAQs on Semicircle

What is Semicircle?

If a circle is cut into half along the diameter, that half-circle is called a semicircle. The two halves are of equal measure. A semicircle can also be referred to as a half-disk and it represents a circular paper plate folded into halves. There is one line of symmetry in the semicircle that is considered as the reflection symmetry. Since the semicircle is the half of a circle which is 360°, hence the arc of the semicircle always measures 180°.

Definition of a Semicircle: When an arc of a circle with its endpoints on the diameter cuts a circle into two equal halves, those halves are called semicircles. It is the most common shape we find in real life, for example, the shape of the protractor, speedometer, taco, and so on. The image below represents a semicircle PQR along with the arc and the diameter (PQ) with both endpoints. Here, point J is the center, and PJ and JQ are the radii of the semicircle.

Now, let us look at some important properties of a semicircle.

Properties of Semicircle

Listed below are a few important properties of a semicircle that makes it a unique shape in geometry:

• A semicircle is a closed 2D shape.
• It is not a polygon since it has a curved edge.
• A semicircle has one curved edge which is its circumference and 1 straight edge which is called its diameter.
• It is exactly half of the circle. The diameter of the circle and the two semicircles formed out of it are the same.
• The area of a semicircle is half of the area of the circle.

Area of a Semicircle

The area of a circle refers to the region or inner space of the circle. Since we know that a semicircle is half a circle, the semicircle area will be half of the area of a circle. So, the area of a circle is πR2 where R is the radius of the circle. Hence,

Area of a Semicircle = πR2/ 2 square units

where,

• R is the radius of the semicircle
• π(pi) is 22/7 or 3.142 approximately

Circumference of a Semicircle

The circumference of a semicircle is considered half of the circle's circumference. The circumference of a semicircle is defined as the measurement of the arc that forms a semicircle. It does not include the length of the diameter. As we know that the circumference of the circle formula is 2πR, where R is the radius. Therefore,

Circumference of a Semicircle = 2πR/2 = πR units

Semicircle Perimeter

The perimeter of a semicircle is the sum of its circumference and diameter. It is not similar to the area of the semicircle i.e. the perimeter is not the half perimeter of a circle. In fact, to calculate the perimeter of a semicircle we need to know either the diameter or radius of a circle along with the length of the arc. To determine the length of the arc, we need the circumference of a semicircle. Since the circumference is C = πR, where C is the circumference, and R is the radius, we can determine the formula for the perimeter of a semicircle which is:

The perimeter of a Semicircle = (πR + 2R) units, or after factoring the R, the perimeter of a semicircle = R(π + 2) units,

where,

• R is the radius of the semicircle
• π(pi) is 22/7 or 3.142 approximately

Angle Inscribed in a Semicircle

The inscribed angle is the angle formed by the line segments drawn from each end of the diameter to any point on the semicircle. No matter where the line touches the semicircle, the angle that is inscribed is always 90°. In the below image, we can see that angle B is at 90 degrees, and the diameter AC is 180°. Since a semicircle is half of a circle, the angle formed by the arc that makes the circle a semicircle measure 180°.

► Related Topics

Listed below are a few interesting topics that are related to semicircle shape in geometry, take a look!

• Circumference to Diameter
• Arc Length
• Chords and Diameters