One of the most common shapes seen in geometry is that of a protractor i.e. a semicircle. 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. In this article, we will be learning more about semicircle, its definition, and the formulas - area and perimeter.
|2.||Area of a Semicircle|
|3.||Perimeter of a Semicircle|
|4.||Circumference of a Semicircle|
|5.||Angle Inscribed in a Semicircle|
|8.||FAQs on Semicircle|
If a circle is cut into half along the diameter, that half is called a semicircle. The two cut halves are of equal measure. A semicircle can also be referred to as a half-disk and it represents a round 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°.
Meaning of a Semicircle
When an arc of a circle with its endpoints on the diameter cut a circle into two equal halves, those halves are called semicircles. It is the most common shape we find in our 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 the endpoints.
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, where R is the radius of the semicircle and π(pi) is 3.142 approximately.
Perimeter of a Semicircle
The perimeter of a semicircle 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 of the semicircle, we need the circumference of a circle. Since the circumference of a circle is C = πd or C = 2πr, where C is the circumference, d is the diameter, 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), where R is the radius of the semicircle and π(pi) is 3.142 approximately.
Circumference of a Semicircle
The circumference of a semicircle is considered the same as the semicircle perimeter as the perimeter is half the circle's circumference. A semicircle consists of a straight line as well which is the diameter of the circle, describing the distance around the shape. Therefore,
Circumference of a Semicircle = πR + 2R units
Angle Inscribed in a Semicircle
The inscribed angle is a line 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 the 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 Articles on Semicircle
Listed below a few interesting topics that are related to a semicircle, take a look!
Example 1: Next to Dan's house is a garden in the shape of a circle with a diameter of 12 yards, Dan wants to use only half the garden for a party, what is the perimeter of the part he wants to use?
Solution: We know that the diameter = 12 yards, we need to find the radius.
Radius = Diameter/2 = 12/2 = 6 yards
So, perimeter of a semicircle = R(π + 2) where π is 3.142
Perimeter = 6 (3.142 + 2)
Perimeter = 6 × 5.142
Perimeter = 30.852 yards
Therefore, the perimeter of half the garden that is going to be used by Dan is 30.852 yards.
Example 2: The radius of Rose's circular cake is 7 units. Find the area of half of the cake.
Solution: We know that the radius = 7 units. The area of a semicircle = πR2/ 2 square units
So, by substituting the value of the radius, Area = ((22/7) × 7 × 7)/2
Area = (22 × 7)/2
Area = 77 square units
Therefore, the area of half of Rose's cake is 77 square units
Example 3: Find the circumference of a semicircle with a diameter of 8 units.
Solution: First, we need to find the radius, radius = diameter/2 = 8/2 = 4 units. The formula to calculate the circumference of a semicircle is the same as the perimeter. Hence,
Circumference = R(π + 2) units
Circumference = 4(3.412 + 2)
Circumference = 4 × 5.412
Circumference = 21.648 units approximately
Therefore, the circumference of the given semicircle is 21.648 units approximately.
FAQs on Semicircle
What is the Meaning of a Semicircle?
A semicircle is half of a circle. An arc within a circle connects from one end to the other forming the diameter that cuts the circle into two equal halves which are the semicircles. We can create two semi-circles from any circle. Some of the real-life examples of a semicircle are the shape of a protractor, the shape of a round paper folded in half, etc.
How do we Calculate the Area of a Semicircle?
The area of a semicircle is the region within the semicircle. It is the exact half of the area of a circle, which is πR2, where R is the length of the radius of the circle. Hence, the area of the semicircle = πR2/ 2.
How do we Calculate the Perimeter of a Semicircle?
The perimeter of a semicircle is not half of a full circle perimeter. Instead, the perimeter and the circumference are the same and to calculate the perimeter of a semicircle we require the length of the arc and the radius or diameter. Hence the formula to calculate the perimeter is Perimeter of a Semicircle = (πR + 2R) units, where R is the length of the radius.
What is the Angle Inscribed in a Semicircle?
The angle inscribed in a semicircle is a line from both the ends of the diameter to any point of the semicircle. The angle inscribed in a semicircle is always 90° or a right angle.
Is Perimeter and Circumference of a Semicircle Similar?
Yes, the perimeter and the circumference of a semicircle are the same. Both represent the boundary length which is the sum of the length of the arc and the diameter of the semicircle.
What is the Diameter of a Semicircle?
Just like a normal circle, the diameter of a semicircle is just twice the radius. If we form a semicircle by cutting a circle into two equal parts, then the diameter of the circle and the two semicircles formed is the same.
What is Half a Semicircle Called?
Half a semicircle is called a quadrant most times. But since a semicircle can be cut into halves in many different ways, there is no specific term for the parts.