Semicircle

Semicircle: In mathematics, particularly in geometry, a semicircle is defined as a one-dimensional set of points that make up half of a circle. It is a circular arc spanning 180 degrees, which is equivalent to π radians, or half of a full rotation. Semicircle is a half circle formed by cutting the circle into two halves. It is a circular arc that measures 180°, or π radians, or a half-turn. It only has one line of symmetry, called reflection symmetry.

In this article, we will discuss the concept of a semicircle, including its shape, formula, examples, perimeter, and area.

What is a Semicircle?

A semicircle is a two-dimensional shape obtained by dividing the circle into two halves along its diameter. In other words, it is the arc of the circle joining the two endpoints of the diameter. The angle formed by the arc is 180° on one side of the diameter. Some semicircle formulas are :

Area of a Semicircle	(πr2)/2
Circumference of a Semicircle	πr
Perimeter of a Semicircle	πr + 2r
Angle in a Semicircle	90°
Central Angle in a Semicircle	180°

Semicircle Definition

A semicircle is a geometric figure that represents half of a circle, formed by dividing a circle along its diameter. It consists of a circular arc and its endpoints, connected by the diameter of the original circle.

Semicircle Shape

If we cut a circle into two halves then the two shapes so formed are called the semicircle. Some real-life examples of the semicircle are the protractor, half moon, half pizza, etc.

Radius of Semicircle

The line segment joining the center of the semicircle to the circumference of the semicircle is called its Radius. In the image added above, OA and OB are radius of semi-circle and OA = OB (r).

Diameter of Semicircle

The line segment joining two points on the circumference of semicircle and passing through the center of the semicircle is called its diameter. A semicircle has one diameter only. In that image added above, AB is the diameter (d) of the circle.

Centroid of Semicircle

Centroid of any closed figure is a point that lies in the middle of the figure, be it centroid of a triangle or any other closed figure. Hence, Centroid of a Semicircle is a point that lies exactly in the middle of the semicircle along the vertical radius of the semicircle.

Let us consider if the center of the semicircle is placed at the origin then x = 0 and from definition we know that centroid of semicircle lies along vertical axis i.e. along the y-axis. In such case the centroid will lie at y = 4r/3π distance from the origin.

Properties of Semicircle

There are several properties of the semicircle. Some of properties of semicircle are,

• Semicircle is a two-dimensional shape.
• Semicircle is half of the circle.
• Semicircle has a curved edge, so it is not a polygon.
• Semicircle is formed by the half of the circumference of the circle and a diameter.
• Angle formed inside a semicircle on its circumference is equal to 90°

Semicircle Formula

There are various semicircle formulas including circumference, area, perimeter of a semicircle. The major formulas for semicircle are :

• Area of a Semicircle
• Perimeter of a Semicircle
• Circumference of a Semicircle

Semicircle Area

Area of the semicircle is given by half of the area of circle because the semicircle is half of the circle. The formula for the area of the semicircle is:

Area of Semicircle = (Area of Circle)/2

Area of Semicircle = (πr²)/2

where,

• r is the Radius of Semicircle
• π = 22 / 7 or 3.14

Area of Semi-Circle is measured in Square Units.

Finding Area of Semicircle

How to find Area of Semicirlce is explained using the example added below,

Find the area of semicircle with radius 14 cm

Area of Semicircle(A) = (πr²)/2

A = (22/7).(14).(14)/2

A = 308 cm²

Learn More :

• Area
• Area of Circle

Circumference of Semicircle

Circumference of the semicircle is given by half of the circumference of circle because semicircle is half of the circle. The formula for the semicircle’s circumference is:

Circumference of Semicircle = (2πr) / 2

Circumference of Semicircle = πr

where,

• r is the Radius of Semicircle
• π = 22 / 7 or 3.14

Semicircle Perimeter

Perimeter of semicircle refers to the sum of the circumference of the semicircle and the diameter of the semicircle. The formula for the perimeter of semicircle is given by:

P_semicircle = Circumference of semicircle + Diameter of semicircle

P_semicircle = πr + d

P_semicircle = πr + 2r, where [d = 2r]

Perimeter of Semicircle = (πr + 2r)

where,

• r is Radius of Semicircle
• π = 22 / 7 or 3.14

Perimeter of Semi-Circle is measured in units such as m, cm, etc.

Learn More: Perimeter

Finding Perimeter of Semicircle

How to find Perimeter of Semicirlce is explained using the example added below,

Find the perimeter of semicircle with radius 14 cm

Perimeter of Semicircle (P) = (π + 2)r

P = (22/7 + 2).14

P = 72 cm

Learn More: Circumference of Circle

Angles in Semicircle

Angle formed by the two lines drawn from the endpoints of the diameter at any point on the semicircle is called as the angle inscribed in a semicircle. Angle inscribed in a semicircle is equal to 90° i.e., right angle. The diameter of semicircle has an angle of 180°as it is a straight line.

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• Geometric Shapes
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Semicircle Examples

Some examples related to semicircle are,

Example 1: Find the perimeter of semicircle if diameter of semicircle is 4cm.

Solution:

Given,

• d = 4 cm

Perimeter of Semicircle(P) = (πr + d)

r = d / 2 = 4/2 = 2 cm

P = (2π + 4) cm

P = 2(π + 2) cm

P = 10.28 cm

Example 2: Find the area of semicircle with radius 5 cm.

Solution:

Given,

• Radius = 5 cm

Area of Semicircle(A) = [πr²] / 2

A = [π(5)²]/2

A = [25π]/2

A = 39.25 cm²

Example 3: Find the circumference of semicircle if the diameter of semicircle is 8 cm.

Solution:

Diameter(d) = 8 cm

Circumference of Semicircle(C) = πr

Radius of Semicircle(r) = d / 2 = 8 / 2 = 4 cm

C = π(4)

C = 12.56 cm

Example 4: Find the diamter of semicircle whose area is 157cm².

Solution:

Given,

• Area of Semicirlce = 157 cm²

Area of Semicircle = [πr²] / 2

157 = [πr²]/2

314 = [πr²]

r² = 314/π

r² = 314/3.14

r² = 100

Radius of Semicircle(r) = 10 cm

Example 5: Find the radius if the circumference of semicircle is 314 cm.

Solution:

Given,

• Circumference(C) = 314 cm

Circumference of Semicircle = πr

Radius of semicircle(r) = 314/3.14

r = 100 cm

Example 6: The radius of semicircle is given 2 cm find its perimeter.

Solution:

Given,

• Radius of Semicircle(r) = 2 cm

Perimeter of Semicircle(P) = r[π + 2]

P = 2[π + 2]

P = 10.28 cm

Practice Problems on Semicircle

Various practice problems related to semicircle are,

Q1. Find the area of semicircle, given the radius of semicircle is 3cm.

Q2. Find the circumference of semicircle if the radius of the semicircle is 5cm.

Q3. Given the circumference of semicircle 4cm and diameter is 3cm. Find the perimeter of semicircle.

Q4. Find the perimeter of the semicircle, given the radius of semicircle is 6cm.

FAQs on Semicircle

Define Semicircle.

Semicircle is defined as a 2-D figure that is formed when a circle is cut into two halves along its diameter. The shape of the protractor in the geometry box is the shape that resembles the semicircle.

How many Sides in Semicircle?

A semicircle has two sides, one curved side, and one flat side.

What is Perimeter of Semicircle Formula?

Formula of perimeter of semicircle is determined by the sum of the circumference and the diameter of the semicircle. For a semicircle with radius (r) unit, perimeter of the semicircle is given by, Perimeter of Semicircle = (πr + 2r)

What is Area of Semicircle Formula?

Formula for Area of Semicircle with radius r is given by: Area of Semicircle = (πr²)/2

What is Radius of Semicircle?

The line drawn from the center of the semicircle to the circumference of the semicircle is called the radius of a semicircle.

What is Radius of Semicircle Formula?

You can find the radius of semicircle using the following formulas :

• If you know the diameter of the semicircle, the radius is half of this length:
  • Radius = Diameter / 2
• If you know the circumference of the full circle (C), you can use the formula for the circumference of a circle, C= 2πr, to find the radius. For a semicircle, you’d typically have half this circumference, so if you’re working from the curved length of the semicircle, you’d first need to double this to get the full circle’s circumference before applying the formula:
  • Radius = C / (2π)
• If you know the area of the full circle (A), you can use the formula for the area of a circle, A=πr², to find the radius. Again, for a semicircle, if you have the semicircle’s area, you’d need to double it to use this formula:
  • Radius = √(A/π).​

What is Angle Inscribed in Semicircle?

Angle formed by the lines drawn from the endpoints of the diameter to any point on the semicircle is the angle inscribed in a semicircle which is a right angle i.e., 90°.

How To Find Perimeter of Semicircle?

Perimeter is the sum of all the boundaries. The perimeter of a semicircle is the sum of the circumference of semicircle and the diameter of the semicircle.

What is Centroid of Semicircle?

Centroid of a Semicircle is a point that lies exactly in the middle of the semicircle along its vertical radius at a distance 4r/3π from the center of the semicircle.