How to Find the Area and Perimeter of the Semicircle?

A semicircle is a semicircle. It is a two-dimensional shape that is formed when a circle is cut into two equal parts. In this step-by-step guide, you will learn how to find the area and perimeter of the semicircle.

How to Find the Area and Perimeter of the Semicircle?

The circumference of a semicircle is the length of the arc that is half of the circle’s circumference, and the perimeter of a semicircle is the sum of its circumference and diameter.

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Step by step guide to finding the area and perimeter of the semicircle

If a circle is cut in half along the diameter, that half-circle is called a semicircle. The two halves are equal in size. A semicircle can also be called a half-disk and represents a circular paper plate folded into halves. There is a line of symmetry in the semicircle which is considered the reflection symmetry. Since a semicircle is half a circle, which is \(360°\), the semicircle arc is always \(180°\).

The image below shows a semicircle \(PQR\) along 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.

Properties of semicircle

Here are some important features of a semicircle that make it unique in geometry:

  • The semicircle is a closed two-dimensional shape.
  • It is not a polygon because 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’s exactly half a circle. The diameter of a circle and two semicircles consisting of it are the same.
  • The area of a semicircle is half the area of a circle.

Area of a semicircle

The area of a circle refers to the area or interior space of the circle. Since we know that a semicircle is half a circle, the area of a semicircle will be half the area of a circle.

Area of a semicircle \(=\color{blue}{\frac{πR^2}{2}}\)

where,

\(R\) is the radius of the semicircle

Circumference of a semicircle

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. The circumference of a semicircle is half of the circle’s circumference.

Circumference of a semicircle \(=\color{blue}{\frac{2πR}{2}= πR}\)

Semicircle perimeter

The perimeter of a semicircle is the sum of its circumference and diameter. To calculate the perimeter of a semicircle, we need to know the diameter or radius of the 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 define the formula for the perimeter of a semicircle which is:

The perimeter of a semicircle \(=\color{blue}{(πR + 2R)}\) units, or after factoring the \(R\), the perimeter of a semicircle \(=\color{blue}{R(π + 2)}\)

where,

  • \(R\) is the radius of the semicircle

Finding the Area and Perimeter of the Semicircle – Example 1:

Find the circumference of a semicircle with a diameter of \(10\) units. \(π=3.14\)

Solution:
The diameter is \(=10\) units. So, radius \(= \frac{10}{2} = 5\) units.
The formula to calculate the circumference of a semicircle is \(πR\). Therefore, by substituting the values of \(π\) and radius in this formula, we get:

Circumference \(=3.14× 5\) units

Circumference \(=15.70\) units

Exercises for Finding the Area and Perimeter of the Semicircle

  1.  Calculate the area of a semicircle whose radius is \(8\) inches. \(π=3.14\)
  2. Find the circumference of a semicircle with a diameter of \(46\) inches. \(π=3.14\)
  3. What is the area of the semicircle if the perimeter of the semicircle is \(156\) units?
This image has an empty alt attribute; its file name is answers.png
  1. \(\color{blue}{100. 48 \space in^2}\)
  2. \(\color{blue}{118. 22 \space in^2}\)
  3. \(\color{blue}{1446}\)

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